This code serves as a matlab Library for non-dimensional CRTBP System. Obtains: Lyapunov Orbit and Halo Orbit Parameters. Future Updates: Functions for all symmetric and asymmetric orbits (given in Daniel Grebow's Master's thesis) , Invarient Manifold functions, Resonant Orbit Functions (as in Manninie Gupta's Master's Thesis) and more. Invarient Manifold Code can be found in 3-Body_Problem Code.
Make use of following functions:
LyapOrbitParameters.m
gives the Initial Conditions and other parameters (time period, Eigen Structure, Stability Index etc.) in the non-dimentinal CR3BP of a lyapunov orbit for spacific mu, liberation point and jacobian.LyapOrbitFamilyParameters.m
gives the Initial Conditions and other parameters (time period, Eigen Structure, Stability Index etc.) in the non-dimentinal CR3BP of family of lyapunov orbits for spacific mu and liberation point.HaloOrbitParameters.m
gives the Initial Conditions and other parameters (time period, Eigen Structure, Stability Index etc.) in the non-dimentinal CR3BP of a Halo orbit (northern and Southern should be specified) for spacific mu, liberation point and jacobian.HaloOrbitFamilyParameters.m
gives the Initial Conditions and other parameters (time period, Eigen Structure, Stability Index etc.) in the non-dimentinal CR3BP of family of Halo orbits (northern and Southern should be specified) for spacific mu and liberation point.PeriodicOrbitInvariantMfdsIC.m
returns the Initial Conditions to compute Invariant Manifolds (Stable+/-, Unstable+/-) for a given Periodic Orbit. The direction needs to be taken care of!Integrator.m
make use of this fucntion to compute the final Periodic Orbits
Inputting System Variables
UserDat.Dimension = 3;
UserDat.mu = 0.0121505856;
UserDat.PointLoc = 1;
UserDat.NoOfFam = 50;
UserDat.CorrectionPlot = 1;
G_var = GlobalData(UserDat);
UserDat.PointLoc
specifies which equilibrium points you want the data for? can take 1,2,3 for nowUserDat.CorrectionPlot
can take 1 and 0 specifying if you want differential correction plots or not.
[LyapOrbFam] = LyapOrbitFamilyParameters(UserDat,G_var);
figure()
plot(LyapOrbFam.Energy, LyapOrbFam.time,'-r','LineWidth',2);
figure()
set(0,'DefaultAxesColorOrder',flipud(jet(length(LyapOrbFam.Energy))));
for i = 1:length(LyapOrbFam.Energy)
[t,x] = Integrator(G_var,G_var.IntFunc.EOM,LyapOrbFam.IC(i,:),[0 LyapOrbFam.time(i)],'forward');
plot(x(:,1),x(:,2));hold on; grid on;
end
scatter(1-UserDat.mu,0,'p','filled');
caxis([LyapOrbFam.Energy(end), LyapOrbFam.Energy(1)]);colormap("jet");
colorbar
xlabel('x (ND)')
ylabel('y (ND)')
title('Lyapunov Orbit Family at L1 for mu = 0.01215');
[HaloOrbFam] = HaloOrbitFamilyParameters(UserDat,G_var, 'northern');
figure()
set(0,'DefaultAxesColorOrder',flipud(jet(length(HaloOrbFam.Energy))));
for i = 1:length(HaloOrbFam.Energy)
[t,x] = Integrator(G_var,G_var.IntFunc.EOM,HaloOrbFam.IC(i,:),[0 HaloOrbFam.time(i)],'forward');
plot3(x(:,1),x(:,2),x(:,3));hold on; grid on;
end
scatter3(1-UserDat.mu,0,0,'p','filled');
caxis([HaloOrbFam.Energy(end), HaloOrbFam.Energy(1)]);
colorbar
xlabel('x (ND)')
ylabel('y (ND)')
zlabel('z (ND)')
title('Lyapunov Orbit Family at L1 for mu = 0.01215');
[LyapOrb] = LyapOrbitParameters(UserDat,G_var, 3.17);
ans1 = PeriodicOrbitInvariantMfdsIC(G_var,LyapOrb,80, 'stable',1);
figure()
for i = 1:length(ans1(:,1))
[t,x] = Integrator(G_var,G_var.IntFunc.EOM,ans1(i,1:6),[0 1.5*LyapOrb.time],'backward');
plot(x(:,1),x(:,2),'g');hold on; grid on;
end
scatter(1-UserDat.mu,0,'p','filled','r');
xlabel('x (ND)')
ylabel('y (ND)')
title('Invariant Manifold for L1 Lyapunov Orbit');
subtitle('mu = 0.01215, Jacobian=3.17');
- Dynamical Syatems, the three-body problem and Space Mission Design, Koon, Lo, Marsden, Ross
- Generating Periodic Orbits In CR3BP With Applications To Lunar South Pole Coverage - Daniel Grebow
- Finding Order in Chaos: Resonant Orbits and Poincare Section - Maaninee Gupta
- TADPOLE ORBITS IN THE L4/L5 REGION: CONSTRUCTION AND LINKS TO OTHER FAMILIES OF PERIODIC ORBITS - Alexandre G. Van Anderlecht
- SPACECRAFT TRAJECTORY DESIGN TECHNIQUES USING RESONANT ORBITS - Srianish Vutukuri
- REPRESENTATIONS OF INVARIANT MANIFOLDS FOR APPLICATIONS IN SYSTEM-TO-SYSTEM TRANSFER DESIGN - Christopher E. Patterson
More to be added :
- Halo Orbit for L3
- Vertical Orbit (L1/2/3/4/5)
- Axial Orbit (L1/2/3/4/5)
- Butterfly (L2/?)
- Planar (L4/5)
- Tadpole Orbit, Horseshoe Orbit (L4/5)
- Resonant Orbits
- Bifurcations and More...