Скачать или смотреть Trajectories with Prescribed Itineraries and MATLAB Tutorial, 3-Body Problem Topic 15

To find trajectories with prescribed itineraries, numerical methods are needed, namely for generating periodic orbits and their invariant manifolds. We outline an algorithm for using these methods to generate a trajectory with a prescribed itinerary in the planar CR3BP. An example computation in MATLAB is given for taking a Poincare section of a stable manifold tube on a Lagrangian L1 Lyapunov orbit.

💻 MATLAB Code Live Code File Format (.mlx).
⬇️ Download at https://tinyurl.com/cr3bpmatlab
Look for: cr3bp_tube_manifolds.mlx
Execute the file in MATLAB

▶️ Previous: 3-Body Problem Periodic Orbits & Stable Manifolds using Differential Correction, MATLAB | Topic 14
   • 3-Body Problem Periodic Orbits & Stable Ma...  

▶️ Next: Halo Orbits in 3-Body Problem - Theory and MATLAB Computation, Topic 16
   • Halo Orbits in 3-Body Problem - Theory and...  

▶️ Three-Body Problem Introduction
   • Three Body Problem Introduction: Lecture 1...  

▶️ Related: Applications to Dynamical Astronomy
   • Interplanetary Transport Network: Fast Tra...  

► Reference: Chapter 4, "Construction of Trajectories with Prescribed Itineraries"
of the PDF book:
Dynamical Systems, the Three-Body Problem and Space Mission Design
Koon, Lo, Marsden, Ross (2022)
Download for free at https://ross.aoe.vt.edu/books

► PDF Lecture Notes (Lecture 11 for this video)
https://is.gd/3BodyNotes

The circular restricted 3-body problem (CR3BP) describes the motion of a body moving in the gravitational field of two primaries that are orbiting in a circle about their common center of mass, with trajectories such as Lagrange points, halo orbits, Lyapunov planar orbits, quasi-periodic orbits, quasi-halos, low-energy trajectories, etc.

• The two primaries could be the Earth and Moon, the Sun and Earth, the Sun and Jupiter, etc.

• The mass parameter μ = m2/(m1 + m2) is the main factor determining the type of motion possible for the spacecraft. It is analogous to the Reynold's number Re in fluid mechanics, determining the onset of new types of behavior.

► Dr. Shane Ross is an Aerospace Engineering Professor at Virginia Tech. He has a Caltech PhD, worked at NASA/JPL and Boeing on interplanetary trajectories, and is a world renowned expert in the 3-body problem. He has written a book on the subject (link above).

► Follow me at https://x.com/RossDynamicsLab

► CHAPTERS
0:00 Introduction, Summary
2:35 Find region with desired itinerary for trajectory
6:33 Step 1, Select appropriate energy
7:59 Step 2, Compute Lagrange point eigenvalues & eigenvectors
8:40 Step 3, Compute Lyapunov orbits via numerical continuation
13:39 MATLAB tutorial begins, code provided (see link above)
17:55 Step 4, Compute stable and unstable invariant manifold tubes
23:13 Step 5, Poincare section of tube
29:04 Step 6, Compute other tube Poincare sections
31:52 Step 7, Pick initial condition in intersection of tubes (X,J,S)
34:26 Tube intersection after several circuits about secondary mass
38:15 Temporarily captured satellite of Jupiter
38:22 Longer itinerary construction (X,J,S,J,X)

► Courses & Playlists by Dr. Ross

▶️ 3-Body Problem Orbital Dynamics
https://is.gd/3BodyProblem

▶️ Space Manifolds
https://is.gd/SpaceManifolds

▶️ Space Vehicle Dynamics
https://is.gd/SpaceVehicleDynamics

▶️ Lagrangian & 3D Rigid Body Dynamics
https://is.gd/AnalyticalDynamics

▶️ Nonlinear Dynamics & Chaos
https://is.gd/NonlinearDynamics

▶️ Hamiltonian Dynamics
https://is.gd/AdvancedDynamics

▶️ Center Manifolds, Normal Forms, & Bifurcations
https://is.gd/CenterManifolds

symbolic dynamics Lagrange points space manifolds differential correction single and multiple shooting collocation state transition matrix variational equations tube dynamics

#orbitalmechanics #threebodyproblem #tubedynamics #manifold #periodicorbit #smalehorseshoe #symbolicdynamics #heteroclinic #homoclinic #LagrangePoint #space #CR3BP #3body #3bodyproblem #SpaceManifolds #JamesWebb #NonlinearDynamics #gravity #SpaceTravel #SpaceManifold #DynamicalSystems #solarSystem #NASA #dynamics #celestial #SpaceSuperhighway #InterplanetarySuperhighway #spaceHighway #gravitational #mathematics #dynamicalAstronomy #astronomy #wormhole #physics #chaos #unstable #PeriodicOrbits #HaloOrbit #LibrationPoint #LagrangianPoint #LowEnergy #VirginiaTech #Caltech #JPL #LyapunovOrbit #CelestialMechanics #HamiltonianDynamics #planets #moons #multibody #GatewayStation #LunarGateway #L1gateway #cislunar #cislunarspace #orbitalDynamics #orbitalMechanics #Chaotician #Boeing #JetPropulsionLab #Centaurs #Asteroids #Comets #TrojanAsteroid #Jupiter #JupiterFamily #JupiterFamilyComets #Hildas #quasiHildas #KuiperBelt