├── CR3BP ├── ExampleScript.m ├── celestialLookUp.m ├── jacobiValDiff.m ├── jacobiValue3D.m ├── lagrangePoints.m ├── plotOther.m ├── rotFrame3d.m ├── rotFrame3dSTM.m └── stats2Body.m ├── LICENSE └── README.md /CR3BP/ExampleScript.m: -------------------------------------------------------------------------------- 1 | close all 2 | clear all 3 | clc 4 | %% 5 | %This script is designed to provide an example of how to use different 6 | %functions in the Matlab Astrodynamics Library CR3BP 7 | % 8 | % Ari Rubinsztejn 9 | % www.gereshes.com 10 | % 2019.03.06 11 | 12 | %% Initialization 13 | 14 | [mu,lStar,tStar,sec,prim] = stats2Body("Moon"); % Get some stats for the Earth-Moon System Note the use of a string 15 | 16 | ic=[1-mu,.0455,0,-.5322,.2,0];% Define some initial conditions for our simulation (in the rotating reference frame) 17 | ts=[0,20]; %Timespan of simulation in non-dimensional time 18 | opts=odeset('RelTol',1e-12,'AbsTol',1e-12); 19 | j0=jacobiValue3D(ic,mu);%Calcualtes the intial jacobi value 20 | 21 | 22 | [t,y]=ode45(@(t,x) rotFrame3d(t,x,mu),ts,ic,opts); %Integrate the trajectory 23 | 24 | diffJ = jacobiValDiff(y,mu); 25 | 26 | 27 | %% Plotting the Trajectory and the Change of the Jacobi Value 28 | h0=figure(); 29 | h0.Position=[220.200000000000,630,1083.80000000000,420]; 30 | subplot(1,2,1) 31 | plot(y(:,1),y(:,2),'DisplayName','Spacecraft Trajectory') 32 | plotOther(mu,j0,1) %Plot other 33 | title('Trajectory in the Earth-Moon System') 34 | xlabel('X-Axis (ND)') 35 | ylabel('Y-Axis (ND)') 36 | legend() 37 | subplot(1,2,2) 38 | plot(t,diffJ) 39 | title('Change in Jacobi Value over time') 40 | xlabel('Time (ND)') 41 | ylabel('\Delta Jacobi Value') 42 | grid on 43 | 44 | %% Plotting the Change of Jacobi Value and Distance from Primary Body 45 | 46 | h1=figure(); 47 | plot(t,abs(diffJ)./max(abs(diffJ)),'DisplayName','Absolute \Delta Jacobi Value','LineWidth',2) 48 | hold on 49 | plot(t,sqrt(((y(:,1)-mu).^2)+(y(:,2).^2))./max(sqrt(((y(:,1)-mu).^2)+(y(:,2).^2))),'--','DisplayName','Normalized Distance From Primary','LineWidth',2) 50 | title('Normalized Absolute \Delta Jacobi Value Vs Normalized Distance From Primary') 51 | xlabel('Time (ND') 52 | legend('Location','southeast') 53 | set(gca, 'YScale', 'log') 54 | 55 | %% Plotting the Trajectory Alone 56 | h=figure(); 57 | plot(y(:,1),y(:,2),'DisplayName','Spacecraft Trajectory') 58 | plotOther(mu,j0,1) %Plot other 59 | title('Trajectory in the Earth-Moon System') 60 | xlabel('X-Axis (ND)') 61 | ylabel('Y-Axis (ND)') 62 | legend() -------------------------------------------------------------------------------- /CR3BP/celestialLookUp.m: -------------------------------------------------------------------------------- 1 | function [body] = celestialLookUp(bodyNumberOrName) 2 | %This function takes in the name of a celestial object and returns a cell 3 | %array of pertinent information 4 | % 5 | %Input: 6 | % bodyNumberOrName - String or Int - Body name with first letter capitalized or index number 7 | % 8 | %Output: 9 | % body - 1x9 Cell array - It contains the following fields: Body 10 | % name, Body it's orbiting around, Axial Rotational rate (Rev/Day), 11 | % Equatorial Radius (Km),Gravitational Parameter (Km**3 s**-2), 12 | % Semi-major axis (Km), Orbital Period (days), Eccentricity, Inclination 13 | % of orbit to elliptic (deg) 14 | % 15 | %Ari Rubinsztejn 16 | %www.gereshes.com 17 | %2019.09.01 18 | 19 | %{ 20 | 21 | Raw Data 22 | celestialTables={"Sun",NaN,0.0394010000000000,695700,132712440041.940,NaN,NaN,NaN,NaN;... 23 | "Moon","Earth",0.0366000000000000,1738,4902.80000000000,384400,27.3200000000000,0.0549000000000000,5.14500000000000;... 24 | "Mercury","Sun",0.0170510000000000,2440,22031.7800000000,4902.80000000000,87.9700000000000,0.205647000000000,7.00390000000000;... 25 | "Venus","Sun",-0.00411500000000000,6051.89000000000,324858.590000000,108208441.280000,224.700000000000,0.00679400000000000,3.39449000000000;... 26 | "Earth","Sun",1.00273700000000,6378.14000000000,398600.440000000,149657721.670000,365.260000000000,0.0161920000000000,0.00450000000000000;... 27 | "Mars","Sun",0.974700000000000,3394,42828.3800000000,227937168.370000,686.980000000000,0.0933430000000000,1.84814000000000;... 28 | "Jupiter","Sun",2.41811100000000,71492,126686534.910000,778350260.220000,4332.59000000000,0.0487080000000000,1.30394000000000;... 29 | "Saturn","Sun",2.25220500000000,60268,37931207.8000000,1433203470.67000,10755.7000000000,0.0506630000000000,2.48560000000000;... 30 | "Uranus","Sun",-1.39210890000000,25559,5793951.32000000,2863429878.70000,30685.4000000000,0.0485510000000000,0.771510000000000;... 31 | "Neptune","Sun",1.48975400000000,24766,6835099.50000000,4501859020.15000,60189,0.00718300000000000,1.77740000000000;... 32 | "Pluto","Sun",0.156563000000000,1188.30000000000,869.340000000000,6018076570.89000,91101.5000000000,0.258313000000000,17.2252400000000;... 33 | "Charon","Pluto",0.156250000000000,605,102.270000000000,19596.8400000000,6.39000000000000,5.00000000000000e-05,112.895960000000;... 34 | "Nix","Pluto",0.529100000000000,43.3300000000000,0.000300000000000000,48690,24.8500000000000,0.238214000000000,112.888390000000;... 35 | "Hydra","Pluto",2.32800000000000,65,0.000320000000000000,64738,38.2000000000000,0.00586200000000000,0.242000000000000;... 36 | "Ganymede","Jupiter",1,2634,9891,1070042.80000000,7.15000000000000,0.000600000000000000,0.186000000000000;... 37 | "Titan","Jupiter",1,2575.50000000000,8978.13000000000,1221870,15.9500000000000,0.0288000000000000,0.280000000000000;... 38 | "Titania","Uranus",1,788.900000000000,235.400000000000,435800,8.71000000000000,0.00220000000000000,0.100000000000000;... 39 | "Ceres","Sun",2.64486000000000,469.700000000000,62.6300000000000,413968739.370000,1680.22000000000,0.0761030000000000,10.6007000000000;... 40 | "Enceladus","Saturn",1,252.300000000000,1.21135000000000,238040,1.37021800000000,0.00470000000000000,0.00900000000000000;... 41 | "Phobos","Mars",1,13.1000000000000,0.000721000000000000,9377.20000000000,0.320000000000000,0.0151000000000000,1.08200000000000;... 42 | "Triton","Neptune",1,1352.60000000000,1432.93000000000,354760,5.87685400000000,1.60000000000000e-05,156.834000000000;... 43 | "Callisto","Jupiter",0.0599200000000000,2403,7181.32000000000,1883000,16.6900000000000,0.00700000000000000,0.281000000000000}; 44 | %} 45 | celestialTables={"Sun",'',0.0394010000000000,695700,132712440041.940,NaN,NaN,NaN,NaN;"Moon",'Earth',0.0366000000000000,1738,4902.80000000000,384400,27.3200000000000,0.0549000000000000,5.14500000000000;"Mercury",'Sun',0.0170510000000000,2440,22031.7800000000,4902.80000000000,87.9700000000000,0.205647000000000,7.00390000000000;"Venus",'Sun',-0.00411500000000000,6051.89000000000,324858.590000000,108208441.280000,224.700000000000,0.00679400000000000,3.39449000000000;"Earth",'Sun',1.00273700000000,6378.14000000000,398600.440000000,149657721.670000,365.260000000000,0.0161920000000000,0.00450000000000000;"Mars",'Sun',0.974700000000000,3394,42828.3800000000,227937168.370000,686.980000000000,0.0933430000000000,1.84814000000000;"Jupiter",'Sun',2.41811100000000,71492,126686534.910000,778350260.220000,4332.59000000000,0.0487080000000000,1.30394000000000;"Saturn",'Sun',2.25220500000000,60268,37931207.8000000,1433203470.67000,10755.7000000000,0.0506630000000000,2.48560000000000;"Uranus",'Sun',-1.39210890000000,25559,5793951.32000000,2863429878.70000,30685.4000000000,0.0485510000000000,0.771510000000000;"Neptune",'Sun',1.48975400000000,24766,6835099.50000000,4501859020.15000,60189,0.00718300000000000,1.77740000000000;"Pluto",'Sun',0.156563000000000,1188.30000000000,869.340000000000,6018076570.89000,91101.5000000000,0.258313000000000,17.2252400000000;"Charon",'Pluto',0.156250000000000,605,102.270000000000,19596.8400000000,6.39000000000000,5.00000000000000e-05,112.895960000000;"Nix",'Pluto',0.529100000000000,43.3300000000000,0.000300000000000000,48690,24.8500000000000,0.238214000000000,112.888390000000;"Hydra",'Pluto',2.32800000000000,65,0.000320000000000000,64738,38.2000000000000,0.00586200000000000,0.242000000000000;"Ganymede",'Jupiter',1,2634,9891,1070042.80000000,7.15000000000000,0.000600000000000000,0.186000000000000;"Titan",'Jupiter',1,2575.50000000000,8978.13000000000,1221870,15.9500000000000,0.0288000000000000,0.280000000000000;"Titania",'Uranus',1,788.900000000000,235.400000000000,435800,8.71000000000000,0.00220000000000000,0.100000000000000;"Ceres",'Sun',2.64486000000000,469.700000000000,62.6300000000000,413968739.370000,1680.22000000000,0.0761030000000000,10.6007000000000;"Enceladus",'Saturn',1,252.300000000000,1.21135000000000,238040,1.37021800000000,0.00470000000000000,0.00900000000000000;"Phobos",'Mars',1,13.1000000000000,0.000721000000000000,9377.20000000000,0.320000000000000,0.0151000000000000,1.08200000000000;"Triton",'Neptune',1,1352.60000000000,1432.93000000000,354760,5.87685400000000,1.60000000000000e-05,156.834000000000;"Callisto",'Jupiter',0.0599200000000000,2403,7181.32000000000,1883000,16.6900000000000,0.00700000000000000,0.281000000000000;"Europa",'Jupiter',1,1560,.0032016,670900,3.55118100000000,0.00900000000000000,0.470000000000000}; 46 | [entries,~]=size(celestialTables); 47 | body={}; 48 | if isnumeric(bodyNumberOrName) && abs(bodyNumberOrName)<=entries 49 | body=celestialTables(abs(bodyNumberOrName),:); 50 | elseif isstring(bodyNumberOrName) 51 | for c=1:entries 52 | if strcmp(bodyNumberOrName,celestialTables{c,1}) 53 | 54 | body=celestialTables(c,:); 55 | break 56 | 57 | end 58 | end 59 | else 60 | error('No entry found by that name or index number') 61 | end 62 | 63 | 64 | end 65 | 66 | -------------------------------------------------------------------------------- /CR3BP/jacobiValDiff.m: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gereshes/Matlab-Astrodynamics-Library/0bfaa738aafe6b0a1d1fb49085fcb9bf23ba941d/CR3BP/jacobiValDiff.m -------------------------------------------------------------------------------- /CR3BP/jacobiValue3D.m: -------------------------------------------------------------------------------- 1 | function [jacobiConst] = jacobiValue3D(X,mu) 2 | %This function calculates the jacobi value of a state in the Circular 3 | %Restricted 3-Body Problem (CR3BP) 4 | % 5 | %Inputs 6 | % X - 1x6 Vector - Your current states [x,y,z,xDot,yDot,zDot] 7 | % mu - double - Your systems nondimenisonal mass ratio 8 | % 9 | %Outputs 10 | % jacobiConst - double - The jacobi constant 11 | % 12 | %Notes:For background on the CR3BP I suggest going here 13 | % https://gereshes.com/2018/11/12/dynamics-of-the-3-body-problem/ 14 | % or 15 | % https://gereshes.com/category/math/astrodynamics/cr3bp/ 16 | % 17 | % Ari Rubinsztejn 18 | % www.gereshes.com 19 | % 2018.11.22 20 | 21 | x=X(1); 22 | y=X(2); 23 | z=X(3); 24 | xDot=X(4); 25 | yDot=X(5); 26 | zDot=X(6); 27 | r=sqrt(((x-1+mu).^2)+(y.^2)+(z.^2)); 28 | d=sqrt(((x+mu).^2)+(y.^2)+(z.^2)); 29 | jacobiConst = (x.^2)+(y.^2) +(2*(1-mu)./d)+(2*mu./r)-((xDot.^2)+(yDot.^2)+(zDot.^2)); 30 | end 31 | 32 | -------------------------------------------------------------------------------- /CR3BP/lagrangePoints.m: -------------------------------------------------------------------------------- 1 | function [xPos,yPos,rHill,rHillPrim] = lagrangePoints(mu,itts) 2 | %This function calucaltes the positions of the lagrange points in the rotating frame 3 | %for the Circular Restricted 3-Body Problem (CR3BP) using the hill radius 4 | %approximation 5 | % 6 | %Inputs 7 | % mu - double - Your systems nondimenisonal mass ratio 8 | % itts- integer - Number of itterations you 9 | % 10 | %Outputs 11 | % xPos - 5x1 Vec - x Positions of Lagrange points 12 | % yPos - 5x1 Vec - y Positions of Lagrange points 13 | % rHill - double - Hill radius of the secondary body 14 | % rHillPrim - double - Hill radius of the primary body 15 | % 16 | %Notes:For background on the CR3BP I suggest going here 17 | % 18 | % https://gereshes.com/category/math/astrodynamics/cr3bp/ 19 | % 20 | % Ari Rubinsztejn 21 | % www.gereshes.com 22 | % 2019.03.06 23 | 24 | rHill = (mu/3)^(1/3); 25 | rHillPrim = ((1-mu)/3)^(1/3); 26 | gam1=1; 27 | gam2=1; 28 | 29 | for c=1:itts 30 | gam1=gam1-((rHill/3)^c); 31 | gam2=gam2-((-1^c)*((rHill/3)^c)); 32 | end 33 | gam1=rHill*gam1; 34 | gam2=rHill*gam2; 35 | xL1=(1-mu)-gam1; 36 | xL2=(1-mu)+gam2; 37 | xL3=-(1+(5*mu/12)); 38 | xL4=.5-mu; 39 | xL5=xL4; 40 | 41 | yL1=0; 42 | yL4=sqrt(3)/2; 43 | 44 | xPos=[xL1,xL2,xL3,xL4,xL5]'; 45 | yPos=[yL1,yL1,yL1,yL4,-yL4]'; 46 | 47 | 48 | end 49 | 50 | -------------------------------------------------------------------------------- /CR3BP/plotOther.m: -------------------------------------------------------------------------------- 1 | function plotOther(mu,jacobiValue,filled) 2 | %Function for plotting other general system points of interest. 3 | % 4 | %This function takes in system and trajectoy parameters, computes other 5 | %objects of interest: 6 | % 1) Positions of the bodies 7 | % 2) Zero Velocity Region (ZVC) in the X-Y plane 8 | % 3) Locations of the Lagrange points 9 | %and then plots them on the last graph 10 | % Inputs: 11 | % mu - double - Nondimenstional mass ratio 12 | % jacobiValue - double - Jacobi clue of desired ZVC (put 0 if no ZVC 13 | % desired) 14 | % filled - int - 0 if you want unfilled ZVC's, 1 if you want it 15 | % filled, 2 if you want a solid fill 16 | % Outputs: 17 | % None 18 | % 19 | % Ari Rubinsztejn 20 | % www.gereshes.com 21 | % ari@gereshes.com 22 | % 2019.03.06 23 | 24 | gcf(); 25 | hold on 26 | 27 | 28 | if (jacobiValue==0) %Check if you want a ZVC 29 | 30 | else 31 | samples=1000; 32 | desJac= jacobiValue; 33 | x=linspace(-1.5,1.5,samples); 34 | y=linspace(0,1.5,samples); 35 | holder=NaN(samples,samples); 36 | holderPos=zeros(samples,samples); 37 | eps=.02; 38 | eps=.1; 39 | 40 | for c=1:samples 41 | for d=1:samples 42 | rVec=[x(c),y(d),0]; 43 | tm=jacobiConstZVC(mu,rVec); 44 | if((desJac)>=tm && tm>(desJac*(1-eps))) 45 | 46 | holder(d,c)=tm; 47 | holderPos(d,c)=1; 48 | 49 | else 50 | 51 | end 52 | end 53 | end 54 | if(filled==1) 55 | contourf(x,y,holder,'DisplayName','ZVC','edgecolor','none') 56 | contourf(x,-y,holder,'HandleVisibility','off','edgecolor','none') 57 | elseif(filled==2) 58 | contourf(x,-y,holder*10,'HandleVisibility','off','edgecolor','none') 59 | contourf(x,y,holder,'DisplayName','ZVC','edgecolor','none') 60 | contourf(x,-y,holder,'HandleVisibility','off','edgecolor','none') 61 | else 62 | contour(x,y,holder,'DisplayName','ZVC') 63 | contour(x,-y,holder,'HandleVisibility','off') 64 | end 65 | 66 | 67 | end 68 | 69 | 70 | [xPos,yPos,rSec,rPrim]=lagrangePoints(mu,50); 71 | scatter(xPos,yPos,'+','DisplayName','Lagrange Points') 72 | hold on 73 | % rSec 74 | scatter(1-mu,0,rSec*100,'filled','DisplayName','Secondary','MarkerEdgeColor',[0 .5 .5],... 75 | 'MarkerFaceColor',[0 1 0]) 76 | scatter(-mu,0,rPrim*100,'filled','DisplayName','Primary','MarkerEdgeColor',[0 .5 .5],... 77 | 'MarkerFaceColor',[1 0 0]) 78 | grid on 79 | grid minor 80 | axis([-1.5,1.5,-1.5,1.5]) 81 | daspect([1,1,1]) 82 | end 83 | 84 | 85 | function [jacobiConstVal] = jacobiConstZVC(mu,rVec) 86 | %Calculates the Jacobi constant at a point 87 | x=rVec(1); 88 | y=rVec(2); 89 | z=rVec(3); 90 | d=sqrt(((x+mu)^2)+(y^2)+(z^2)); 91 | r=sqrt(((x-1+mu)^2)+(y^2)+(z^2)); 92 | jacobiConstVal=(x^2)+(y^2)+((2-(2*mu))/d)+(2*mu/r); 93 | end 94 | 95 | -------------------------------------------------------------------------------- /CR3BP/rotFrame3d.m: -------------------------------------------------------------------------------- 1 | function [XNew] = rotFrame3d(t,X,mu) 2 | %CR3BP rotating frame dynamics function, to be used with Matlab ODE suite 3 | % 4 | %Inputs: 5 | % t - double - current time 6 | % X - 6 by 1 vector - Current states [x,y,z,xDot,yDot,zDot]' 7 | % mu- double - Non-Dimensional Mass ratio 8 | % 9 | %Outputs: 10 | % XNew - 6 by 1 vector - Derivative of curent states 11 | % [xDot,yDot,zDot,xDotDot,yDotDot,zDotDot]' 12 | % 13 | % Ari Rubinsztejn 14 | % www.gereshes.com 15 | % 2019.03.06 16 | 17 | %% Unpack variables 18 | x=X(1); 19 | y=X(2); 20 | z=X(3); 21 | xDot=X(4); 22 | yDot=X(5); 23 | zDot=X(6); 24 | 25 | d=sqrt(((x+mu)^2)+(y^2)+(z^2)); 26 | d3=d^3; 27 | r= sqrt(((x-1+mu)^2)+(y^2)+(z^2)); 28 | r3=r^3; 29 | 30 | %% Calculate Updates 31 | xDotDot = (2*yDot)+x - ((1-mu)*(x+mu)/d3)-(mu*(x-1+mu)/(r3)); 32 | yDotDot = (-2*xDot)+y - ((1-mu)*y/d3)-(mu*y/r3); 33 | zDotDot = (-z*(1-mu)/d3) - (mu*z/r3); 34 | XNew=[xDot,yDot,zDot,xDotDot,yDotDot,zDotDot]'; 35 | end 36 | 37 | -------------------------------------------------------------------------------- /CR3BP/rotFrame3dSTM.m: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gereshes/Matlab-Astrodynamics-Library/0bfaa738aafe6b0a1d1fb49085fcb9bf23ba941d/CR3BP/rotFrame3dSTM.m -------------------------------------------------------------------------------- /CR3BP/stats2Body.m: -------------------------------------------------------------------------------- 1 | function [mu,lStar,tStar,sec,prim] = stats2Body(secondaryNameOrIndex) 2 | %This function takes in the name of a celestial object and returns a cell 3 | %array of pertinent information. 4 | % 5 | %Note: See https://gereshes.com/2018/11/12/dynamics-of-the-3-body-problem/ 6 | % for eplanations/calculations of mu,lStar,tStar 7 | % 8 | %Input: 9 | % bodyNumberOrName - String or Int - Body name with first letter capitalized or index number 10 | % 11 | %Output: 12 | % mu- double - Nondimensional mass ratio 13 | % lStar - double - Charachtersitich length (Km) 14 | % tStar - double - Charachteristich time (s) 15 | % sec - 1x9 Cell array - It contains the following fields: Body 16 | % name, Body it's orbiting around, Axial Rotational rate (Rev/Day), 17 | % Equatorial Radius (Km),Gravitational Parameter (Km**3 s**-2), 18 | % Semi-major axis (Km), Orbital Period (days), Eccentricity, Inclination 19 | % of orbit to elliptic (deg), Mass of the planet (Kg) 20 | % prim - 1x9 Cell array - It contains the following fields: Body 21 | % name, Body it's orbiting around, Axial Rotational rate (Rev/Day), 22 | % Equatorial Radius (Km),Gravitational Parameter (Km**3 s**-2), 23 | % Semi-major axis (Km), Orbital Period (days), Eccentricity, Inclination 24 | % of orbit to elliptic (deg), Mass of the planet (Kg) 25 | % 26 | % Ari Rubinsztejn 27 | % www.gereshes.com 28 | % 2019.03.06 29 | 30 | G=6.67408E-20; %Universal gravatational constant (Km**3 Kg**-1 s**-2) 31 | sec=celestialLookUp(secondaryNameOrIndex); 32 | prim=celestialLookUp(string(sec{2})); 33 | mSec = sec{5}/G; 34 | mPrim = prim{5}/G; 35 | prim{10}=mPrim; 36 | sec{10}=mSec; 37 | mStar=mSec+mPrim; 38 | mu=mSec/mStar; 39 | lStar=sec{6}; 40 | tStar=sqrt((lStar.^3)./(G.*mStar)); 41 | end 42 | 43 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. By contrast, 15 | the GNU General Public License is intended to guarantee your freedom to 16 | share and change all versions of a program--to make sure it remains free 17 | software for all its users. We, the Free Software Foundation, use the 18 | GNU General Public License for most of our software; it applies also to 19 | any other work released this way by its authors. You can apply it to 20 | your programs, too. 21 | 22 | When we speak of free software, we are referring to freedom, not 23 | price. Our General Public Licenses are designed to make sure that you 24 | have the freedom to distribute copies of free software (and charge for 25 | them if you wish), that you receive source code or can get it if you 26 | want it, that you can change the software or use pieces of it in new 27 | free programs, and that you know you can do these things. 28 | 29 | To protect your rights, we need to prevent others from denying you 30 | these rights or asking you to surrender the rights. Therefore, you have 31 | certain responsibilities if you distribute copies of the software, or if 32 | you modify it: responsibilities to respect the freedom of others. 33 | 34 | For example, if you distribute copies of such a program, whether 35 | gratis or for a fee, you must pass on to the recipients the same 36 | freedoms that you received. You must make sure that they, too, receive 37 | or can get the source code. And you must show them these terms so they 38 | know their rights. 39 | 40 | Developers that use the GNU GPL protect your rights with two steps: 41 | (1) assert copyright on the software, and (2) offer you this License 42 | giving you legal permission to copy, distribute and/or modify it. 43 | 44 | For the developers' and authors' protection, the GPL clearly explains 45 | that there is no warranty for this free software. For both users' and 46 | authors' sake, the GPL requires that modified versions be marked as 47 | changed, so that their problems will not be attributed erroneously to 48 | authors of previous versions. 49 | 50 | Some devices are designed to deny users access to install or run 51 | modified versions of the software inside them, although the manufacturer 52 | can do so. This is fundamentally incompatible with the aim of 53 | protecting users' freedom to change the software. The systematic 54 | pattern of such abuse occurs in the area of products for individuals to 55 | use, which is precisely where it is most unacceptable. Therefore, we 56 | have designed this version of the GPL to prohibit the practice for those 57 | products. If such problems arise substantially in other domains, we 58 | stand ready to extend this provision to those domains in future versions 59 | of the GPL, as needed to protect the freedom of users. 60 | 61 | Finally, every program is threatened constantly by software patents. 62 | States should not allow patents to restrict development and use of 63 | software on general-purpose computers, but in those that do, we wish to 64 | avoid the special danger that patents applied to a free program could 65 | make it effectively proprietary. To prevent this, the GPL assures that 66 | patents cannot be used to render the program non-free. 67 | 68 | The precise terms and conditions for copying, distribution and 69 | modification follow. 70 | 71 | TERMS AND CONDITIONS 72 | 73 | 0. Definitions. 74 | 75 | "This License" refers to version 3 of the GNU General Public License. 76 | 77 | "Copyright" also means copyright-like laws that apply to other kinds of 78 | works, such as semiconductor masks. 79 | 80 | "The Program" refers to any copyrightable work licensed under this 81 | License. Each licensee is addressed as "you". "Licensees" and 82 | "recipients" may be individuals or organizations. 83 | 84 | To "modify" a work means to copy from or adapt all or part of the work 85 | in a fashion requiring copyright permission, other than the making of an 86 | exact copy. The resulting work is called a "modified version" of the 87 | earlier work or a work "based on" the earlier work. 88 | 89 | A "covered work" means either the unmodified Program or a work based 90 | on the Program. 91 | 92 | To "propagate" a work means to do anything with it that, without 93 | permission, would make you directly or secondarily liable for 94 | infringement under applicable copyright law, except executing it on a 95 | computer or modifying a private copy. Propagation includes copying, 96 | distribution (with or without modification), making available to the 97 | public, and in some countries other activities as well. 98 | 99 | To "convey" a work means any kind of propagation that enables other 100 | parties to make or receive copies. Mere interaction with a user through 101 | a computer network, with no transfer of a copy, is not conveying. 102 | 103 | An interactive user interface displays "Appropriate Legal Notices" 104 | to the extent that it includes a convenient and prominently visible 105 | feature that (1) displays an appropriate copyright notice, and (2) 106 | tells the user that there is no warranty for the work (except to the 107 | extent that warranties are provided), that licensees may convey the 108 | work under this License, and how to view a copy of this License. If 109 | the interface presents a list of user commands or options, such as a 110 | menu, a prominent item in the list meets this criterion. 111 | 112 | 1. Source Code. 113 | 114 | The "source code" for a work means the preferred form of the work 115 | for making modifications to it. "Object code" means any non-source 116 | form of a work. 117 | 118 | A "Standard Interface" means an interface that either is an official 119 | standard defined by a recognized standards body, or, in the case of 120 | interfaces specified for a particular programming language, one that 121 | is widely used among developers working in that language. 122 | 123 | The "System Libraries" of an executable work include anything, other 124 | than the work as a whole, that (a) is included in the normal form of 125 | packaging a Major Component, but which is not part of that Major 126 | Component, and (b) serves only to enable use of the work with that 127 | Major Component, or to implement a Standard Interface for which an 128 | implementation is available to the public in source code form. A 129 | "Major Component", in this context, means a major essential component 130 | (kernel, window system, and so on) of the specific operating system 131 | (if any) on which the executable work runs, or a compiler used to 132 | produce the work, or an object code interpreter used to run it. 133 | 134 | The "Corresponding Source" for a work in object code form means all 135 | the source code needed to generate, install, and (for an executable 136 | work) run the object code and to modify the work, including scripts to 137 | control those activities. However, it does not include the work's 138 | System Libraries, or general-purpose tools or generally available free 139 | programs which are used unmodified in performing those activities but 140 | which are not part of the work. For example, Corresponding Source 141 | includes interface definition files associated with source files for 142 | the work, and the source code for shared libraries and dynamically 143 | linked subprograms that the work is specifically designed to require, 144 | such as by intimate data communication or control flow between those 145 | subprograms and other parts of the work. 146 | 147 | The Corresponding Source need not include anything that users 148 | can regenerate automatically from other parts of the Corresponding 149 | Source. 150 | 151 | The Corresponding Source for a work in source code form is that 152 | same work. 153 | 154 | 2. Basic Permissions. 155 | 156 | All rights granted under this License are granted for the term of 157 | copyright on the Program, and are irrevocable provided the stated 158 | conditions are met. This License explicitly affirms your unlimited 159 | permission to run the unmodified Program. The output from running a 160 | covered work is covered by this License only if the output, given its 161 | content, constitutes a covered work. This License acknowledges your 162 | rights of fair use or other equivalent, as provided by copyright law. 163 | 164 | You may make, run and propagate covered works that you do not 165 | convey, without conditions so long as your license otherwise remains 166 | in force. You may convey covered works to others for the sole purpose 167 | of having them make modifications exclusively for you, or provide you 168 | with facilities for running those works, provided that you comply with 169 | the terms of this License in conveying all material for which you do 170 | not control copyright. Those thus making or running the covered works 171 | for you must do so exclusively on your behalf, under your direction 172 | and control, on terms that prohibit them from making any copies of 173 | your copyrighted material outside their relationship with you. 174 | 175 | Conveying under any other circumstances is permitted solely under 176 | the conditions stated below. Sublicensing is not allowed; section 10 177 | makes it unnecessary. 178 | 179 | 3. Protecting Users' Legal Rights From Anti-Circumvention Law. 180 | 181 | No covered work shall be deemed part of an effective technological 182 | measure under any applicable law fulfilling obligations under article 183 | 11 of the WIPO copyright treaty adopted on 20 December 1996, or 184 | similar laws prohibiting or restricting circumvention of such 185 | measures. 186 | 187 | When you convey a covered work, you waive any legal power to forbid 188 | circumvention of technological measures to the extent such circumvention 189 | is effected by exercising rights under this License with respect to 190 | the covered work, and you disclaim any intention to limit operation or 191 | modification of the work as a means of enforcing, against the work's 192 | users, your or third parties' legal rights to forbid circumvention of 193 | technological measures. 194 | 195 | 4. Conveying Verbatim Copies. 196 | 197 | You may convey verbatim copies of the Program's source code as you 198 | receive it, in any medium, provided that you conspicuously and 199 | appropriately publish on each copy an appropriate copyright notice; 200 | keep intact all notices stating that this License and any 201 | non-permissive terms added in accord with section 7 apply to the code; 202 | keep intact all notices of the absence of any warranty; and give all 203 | recipients a copy of this License along with the Program. 204 | 205 | You may charge any price or no price for each copy that you convey, 206 | and you may offer support or warranty protection for a fee. 207 | 208 | 5. Conveying Modified Source Versions. 209 | 210 | You may convey a work based on the Program, or the modifications to 211 | produce it from the Program, in the form of source code under the 212 | terms of section 4, provided that you also meet all of these conditions: 213 | 214 | a) The work must carry prominent notices stating that you modified 215 | it, and giving a relevant date. 216 | 217 | b) The work must carry prominent notices stating that it is 218 | released under this License and any conditions added under section 219 | 7. This requirement modifies the requirement in section 4 to 220 | "keep intact all notices". 221 | 222 | c) You must license the entire work, as a whole, under this 223 | License to anyone who comes into possession of a copy. This 224 | License will therefore apply, along with any applicable section 7 225 | additional terms, to the whole of the work, and all its parts, 226 | regardless of how they are packaged. This License gives no 227 | permission to license the work in any other way, but it does not 228 | invalidate such permission if you have separately received it. 229 | 230 | d) If the work has interactive user interfaces, each must display 231 | Appropriate Legal Notices; however, if the Program has interactive 232 | interfaces that do not display Appropriate Legal Notices, your 233 | work need not make them do so. 234 | 235 | A compilation of a covered work with other separate and independent 236 | works, which are not by their nature extensions of the covered work, 237 | and which are not combined with it such as to form a larger program, 238 | in or on a volume of a storage or distribution medium, is called an 239 | "aggregate" if the compilation and its resulting copyright are not 240 | used to limit the access or legal rights of the compilation's users 241 | beyond what the individual works permit. Inclusion of a covered work 242 | in an aggregate does not cause this License to apply to the other 243 | parts of the aggregate. 244 | 245 | 6. Conveying Non-Source Forms. 246 | 247 | You may convey a covered work in object code form under the terms 248 | of sections 4 and 5, provided that you also convey the 249 | machine-readable Corresponding Source under the terms of this License, 250 | in one of these ways: 251 | 252 | a) Convey the object code in, or embodied in, a physical product 253 | (including a physical distribution medium), accompanied by the 254 | Corresponding Source fixed on a durable physical medium 255 | customarily used for software interchange. 256 | 257 | b) Convey the object code in, or embodied in, a physical product 258 | (including a physical distribution medium), accompanied by a 259 | written offer, valid for at least three years and valid for as 260 | long as you offer spare parts or customer support for that product 261 | model, to give anyone who possesses the object code either (1) a 262 | copy of the Corresponding Source for all the software in the 263 | product that is covered by this License, on a durable physical 264 | medium customarily used for software interchange, for a price no 265 | more than your reasonable cost of physically performing this 266 | conveying of source, or (2) access to copy the 267 | Corresponding Source from a network server at no charge. 268 | 269 | c) Convey individual copies of the object code with a copy of the 270 | written offer to provide the Corresponding Source. This 271 | alternative is allowed only occasionally and noncommercially, and 272 | only if you received the object code with such an offer, in accord 273 | with subsection 6b. 274 | 275 | d) Convey the object code by offering access from a designated 276 | place (gratis or for a charge), and offer equivalent access to the 277 | Corresponding Source in the same way through the same place at no 278 | further charge. You need not require recipients to copy the 279 | Corresponding Source along with the object code. If the place to 280 | copy the object code is a network server, the Corresponding Source 281 | may be on a different server (operated by you or a third party) 282 | that supports equivalent copying facilities, provided you maintain 283 | clear directions next to the object code saying where to find the 284 | Corresponding Source. Regardless of what server hosts the 285 | Corresponding Source, you remain obligated to ensure that it is 286 | available for as long as needed to satisfy these requirements. 287 | 288 | e) Convey the object code using peer-to-peer transmission, provided 289 | you inform other peers where the object code and Corresponding 290 | Source of the work are being offered to the general public at no 291 | charge under subsection 6d. 292 | 293 | A separable portion of the object code, whose source code is excluded 294 | from the Corresponding Source as a System Library, need not be 295 | included in conveying the object code work. 296 | 297 | A "User Product" is either (1) a "consumer product", which means any 298 | tangible personal property which is normally used for personal, family, 299 | or household purposes, or (2) anything designed or sold for incorporation 300 | into a dwelling. In determining whether a product is a consumer product, 301 | doubtful cases shall be resolved in favor of coverage. For a particular 302 | product received by a particular user, "normally used" refers to a 303 | typical or common use of that class of product, regardless of the status 304 | of the particular user or of the way in which the particular user 305 | actually uses, or expects or is expected to use, the product. A product 306 | is a consumer product regardless of whether the product has substantial 307 | commercial, industrial or non-consumer uses, unless such uses represent 308 | the only significant mode of use of the product. 309 | 310 | "Installation Information" for a User Product means any methods, 311 | procedures, authorization keys, or other information required to install 312 | and execute modified versions of a covered work in that User Product from 313 | a modified version of its Corresponding Source. The information must 314 | suffice to ensure that the continued functioning of the modified object 315 | code is in no case prevented or interfered with solely because 316 | modification has been made. 317 | 318 | If you convey an object code work under this section in, or with, or 319 | specifically for use in, a User Product, and the conveying occurs as 320 | part of a transaction in which the right of possession and use of the 321 | User Product is transferred to the recipient in perpetuity or for a 322 | fixed term (regardless of how the transaction is characterized), the 323 | Corresponding Source conveyed under this section must be accompanied 324 | by the Installation Information. But this requirement does not apply 325 | if neither you nor any third party retains the ability to install 326 | modified object code on the User Product (for example, the work has 327 | been installed in ROM). 328 | 329 | The requirement to provide Installation Information does not include a 330 | requirement to continue to provide support service, warranty, or updates 331 | for a work that has been modified or installed by the recipient, or for 332 | the User Product in which it has been modified or installed. Access to a 333 | network may be denied when the modification itself materially and 334 | adversely affects the operation of the network or violates the rules and 335 | protocols for communication across the network. 336 | 337 | Corresponding Source conveyed, and Installation Information provided, 338 | in accord with this section must be in a format that is publicly 339 | documented (and with an implementation available to the public in 340 | source code form), and must require no special password or key for 341 | unpacking, reading or copying. 342 | 343 | 7. Additional Terms. 344 | 345 | "Additional permissions" are terms that supplement the terms of this 346 | License by making exceptions from one or more of its conditions. 347 | Additional permissions that are applicable to the entire Program shall 348 | be treated as though they were included in this License, to the extent 349 | that they are valid under applicable law. If additional permissions 350 | apply only to part of the Program, that part may be used separately 351 | under those permissions, but the entire Program remains governed by 352 | this License without regard to the additional permissions. 353 | 354 | When you convey a copy of a covered work, you may at your option 355 | remove any additional permissions from that copy, or from any part of 356 | it. (Additional permissions may be written to require their own 357 | removal in certain cases when you modify the work.) You may place 358 | additional permissions on material, added by you to a covered work, 359 | for which you have or can give appropriate copyright permission. 360 | 361 | Notwithstanding any other provision of this License, for material you 362 | add to a covered work, you may (if authorized by the copyright holders of 363 | that material) supplement the terms of this License with terms: 364 | 365 | a) Disclaiming warranty or limiting liability differently from the 366 | terms of sections 15 and 16 of this License; or 367 | 368 | b) Requiring preservation of specified reasonable legal notices or 369 | author attributions in that material or in the Appropriate Legal 370 | Notices displayed by works containing it; or 371 | 372 | c) Prohibiting misrepresentation of the origin of that material, or 373 | requiring that modified versions of such material be marked in 374 | reasonable ways as different from the original version; or 375 | 376 | d) Limiting the use for publicity purposes of names of licensors or 377 | authors of the material; or 378 | 379 | e) Declining to grant rights under trademark law for use of some 380 | trade names, trademarks, or service marks; or 381 | 382 | f) Requiring indemnification of licensors and authors of that 383 | material by anyone who conveys the material (or modified versions of 384 | it) with contractual assumptions of liability to the recipient, for 385 | any liability that these contractual assumptions directly impose on 386 | those licensors and authors. 387 | 388 | All other non-permissive additional terms are considered "further 389 | restrictions" within the meaning of section 10. If the Program as you 390 | received it, or any part of it, contains a notice stating that it is 391 | governed by this License along with a term that is a further 392 | restriction, you may remove that term. If a license document contains 393 | a further restriction but permits relicensing or conveying under this 394 | License, you may add to a covered work material governed by the terms 395 | of that license document, provided that the further restriction does 396 | not survive such relicensing or conveying. 397 | 398 | If you add terms to a covered work in accord with this section, you 399 | must place, in the relevant source files, a statement of the 400 | additional terms that apply to those files, or a notice indicating 401 | where to find the applicable terms. 402 | 403 | Additional terms, permissive or non-permissive, may be stated in the 404 | form of a separately written license, or stated as exceptions; 405 | the above requirements apply either way. 406 | 407 | 8. Termination. 408 | 409 | You may not propagate or modify a covered work except as expressly 410 | provided under this License. Any attempt otherwise to propagate or 411 | modify it is void, and will automatically terminate your rights under 412 | this License (including any patent licenses granted under the third 413 | paragraph of section 11). 414 | 415 | However, if you cease all violation of this License, then your 416 | license from a particular copyright holder is reinstated (a) 417 | provisionally, unless and until the copyright holder explicitly and 418 | finally terminates your license, and (b) permanently, if the copyright 419 | holder fails to notify you of the violation by some reasonable means 420 | prior to 60 days after the cessation. 421 | 422 | Moreover, your license from a particular copyright holder is 423 | reinstated permanently if the copyright holder notifies you of the 424 | violation by some reasonable means, this is the first time you have 425 | received notice of violation of this License (for any work) from that 426 | copyright holder, and you cure the violation prior to 30 days after 427 | your receipt of the notice. 428 | 429 | Termination of your rights under this section does not terminate the 430 | licenses of parties who have received copies or rights from you under 431 | this License. If your rights have been terminated and not permanently 432 | reinstated, you do not qualify to receive new licenses for the same 433 | material under section 10. 434 | 435 | 9. Acceptance Not Required for Having Copies. 436 | 437 | You are not required to accept this License in order to receive or 438 | run a copy of the Program. Ancillary propagation of a covered work 439 | occurring solely as a consequence of using peer-to-peer transmission 440 | to receive a copy likewise does not require acceptance. However, 441 | nothing other than this License grants you permission to propagate or 442 | modify any covered work. These actions infringe copyright if you do 443 | not accept this License. Therefore, by modifying or propagating a 444 | covered work, you indicate your acceptance of this License to do so. 445 | 446 | 10. Automatic Licensing of Downstream Recipients. 447 | 448 | Each time you convey a covered work, the recipient automatically 449 | receives a license from the original licensors, to run, modify and 450 | propagate that work, subject to this License. You are not responsible 451 | for enforcing compliance by third parties with this License. 452 | 453 | An "entity transaction" is a transaction transferring control of an 454 | organization, or substantially all assets of one, or subdividing an 455 | organization, or merging organizations. If propagation of a covered 456 | work results from an entity transaction, each party to that 457 | transaction who receives a copy of the work also receives whatever 458 | licenses to the work the party's predecessor in interest had or could 459 | give under the previous paragraph, plus a right to possession of the 460 | Corresponding Source of the work from the predecessor in interest, if 461 | the predecessor has it or can get it with reasonable efforts. 462 | 463 | You may not impose any further restrictions on the exercise of the 464 | rights granted or affirmed under this License. For example, you may 465 | not impose a license fee, royalty, or other charge for exercise of 466 | rights granted under this License, and you may not initiate litigation 467 | (including a cross-claim or counterclaim in a lawsuit) alleging that 468 | any patent claim is infringed by making, using, selling, offering for 469 | sale, or importing the Program or any portion of it. 470 | 471 | 11. Patents. 472 | 473 | A "contributor" is a copyright holder who authorizes use under this 474 | License of the Program or a work on which the Program is based. The 475 | work thus licensed is called the contributor's "contributor version". 476 | 477 | A contributor's "essential patent claims" are all patent claims 478 | owned or controlled by the contributor, whether already acquired or 479 | hereafter acquired, that would be infringed by some manner, permitted 480 | by this License, of making, using, or selling its contributor version, 481 | but do not include claims that would be infringed only as a 482 | consequence of further modification of the contributor version. For 483 | purposes of this definition, "control" includes the right to grant 484 | patent sublicenses in a manner consistent with the requirements of 485 | this License. 486 | 487 | Each contributor grants you a non-exclusive, worldwide, royalty-free 488 | patent license under the contributor's essential patent claims, to 489 | make, use, sell, offer for sale, import and otherwise run, modify and 490 | propagate the contents of its contributor version. 491 | 492 | In the following three paragraphs, a "patent license" is any express 493 | agreement or commitment, however denominated, not to enforce a patent 494 | (such as an express permission to practice a patent or covenant not to 495 | sue for patent infringement). To "grant" such a patent license to a 496 | party means to make such an agreement or commitment not to enforce a 497 | patent against the party. 498 | 499 | If you convey a covered work, knowingly relying on a patent license, 500 | and the Corresponding Source of the work is not available for anyone 501 | to copy, free of charge and under the terms of this License, through a 502 | publicly available network server or other readily accessible means, 503 | then you must either (1) cause the Corresponding Source to be so 504 | available, or (2) arrange to deprive yourself of the benefit of the 505 | patent license for this particular work, or (3) arrange, in a manner 506 | consistent with the requirements of this License, to extend the patent 507 | license to downstream recipients. "Knowingly relying" means you have 508 | actual knowledge that, but for the patent license, your conveying the 509 | covered work in a country, or your recipient's use of the covered work 510 | in a country, would infringe one or more identifiable patents in that 511 | country that you have reason to believe are valid. 512 | 513 | If, pursuant to or in connection with a single transaction or 514 | arrangement, you convey, or propagate by procuring conveyance of, a 515 | covered work, and grant a patent license to some of the parties 516 | receiving the covered work authorizing them to use, propagate, modify 517 | or convey a specific copy of the covered work, then the patent license 518 | you grant is automatically extended to all recipients of the covered 519 | work and works based on it. 520 | 521 | A patent license is "discriminatory" if it does not include within 522 | the scope of its coverage, prohibits the exercise of, or is 523 | conditioned on the non-exercise of one or more of the rights that are 524 | specifically granted under this License. You may not convey a covered 525 | work if you are a party to an arrangement with a third party that is 526 | in the business of distributing software, under which you make payment 527 | to the third party based on the extent of your activity of conveying 528 | the work, and under which the third party grants, to any of the 529 | parties who would receive the covered work from you, a discriminatory 530 | patent license (a) in connection with copies of the covered work 531 | conveyed by you (or copies made from those copies), or (b) primarily 532 | for and in connection with specific products or compilations that 533 | contain the covered work, unless you entered into that arrangement, 534 | or that patent license was granted, prior to 28 March 2007. 535 | 536 | Nothing in this License shall be construed as excluding or limiting 537 | any implied license or other defenses to infringement that may 538 | otherwise be available to you under applicable patent law. 539 | 540 | 12. No Surrender of Others' Freedom. 541 | 542 | If conditions are imposed on you (whether by court order, agreement or 543 | otherwise) that contradict the conditions of this License, they do not 544 | excuse you from the conditions of this License. If you cannot convey a 545 | covered work so as to satisfy simultaneously your obligations under this 546 | License and any other pertinent obligations, then as a consequence you may 547 | not convey it at all. For example, if you agree to terms that obligate you 548 | to collect a royalty for further conveying from those to whom you convey 549 | the Program, the only way you could satisfy both those terms and this 550 | License would be to refrain entirely from conveying the Program. 551 | 552 | 13. Use with the GNU Affero General Public License. 553 | 554 | Notwithstanding any other provision of this License, you have 555 | permission to link or combine any covered work with a work licensed 556 | under version 3 of the GNU Affero General Public License into a single 557 | combined work, and to convey the resulting work. The terms of this 558 | License will continue to apply to the part which is the covered work, 559 | but the special requirements of the GNU Affero General Public License, 560 | section 13, concerning interaction through a network will apply to the 561 | combination as such. 562 | 563 | 14. Revised Versions of this License. 564 | 565 | The Free Software Foundation may publish revised and/or new versions of 566 | the GNU General Public License from time to time. Such new versions will 567 | be similar in spirit to the present version, but may differ in detail to 568 | address new problems or concerns. 569 | 570 | Each version is given a distinguishing version number. If the 571 | Program specifies that a certain numbered version of the GNU General 572 | Public License "or any later version" applies to it, you have the 573 | option of following the terms and conditions either of that numbered 574 | version or of any later version published by the Free Software 575 | Foundation. If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Matlab-Astrodynamics-Library 2 | [![View Matlab-Astrodynamics-Library on File Exchange](https://www.mathworks.com/matlabcentral/images/matlab-file-exchange.svg)](https://www.mathworks.com/matlabcentral/fileexchange/74035-matlab-astrodynamics-library) 3 | A repo of matlab functions related to astrodynamics. See https://wp.me/P9p1J9-H8 for more details 4 | --------------------------------------------------------------------------------