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Orbital dynamics beyond GEO is best described by a restricted 3-body model, where a spacecraft, asteroid, or piece of debris is affected by both the Earth and Moon simultaneously. We tell you the basics here. The orbital dynamics in this regime (xGEO or cislunar space), encompassing secular, resonant, chaotic, close-encounter, and manifold dynamics, is dramatically different than the weakly perturbed Keplerian approach used for over a half century for the detection and tracking of objects near Earth. We review the foundational dynamics in the entire xGEO regime, including lunar mean motion resonances (MMRs) and short timescale dynamics of libration-point orbits (LPOs) and their invariant manifolds. Whereas circumterrestrial and circumlunar orbits are largely governed by the perturbed two-body problem, in which the effects of the non-spherical gravity field and third-body perturbations on Earth or Moon satellites are often treated in a 'local' perturbative formulation, all other cislunar trajectories, including lunar transfers and LPOs, are applications of the 'global' gravitational N-body problem. Trans-lunar trajectories are governed by the restricted three-body problem (R3BP), in which the spacecraft of negligible mass is simultaneously affected by the terrestrial and lunar gravitational forces. This framework efficiently captures Earth-Moon orbital transfers, models the regions of the Lagrange equilibrium points, and has generally been the most studied formulation of motion in cislunar space. 💻 MATLAB Code Live Code File Format (.mlx). At the following link, https://tinyurl.com/cr3bpmatlab ⬇️ Download cr3bp_differential_correction.mlx You can then execute the Live Script in MATLAB This is the basic idea behind differential correction: making a small change at one end to target to a desired point at the other end. We use the state transition matrix. ► CHAPTERS 0:00 Cislunar Space Introduction 1:08 Example low-energy Cislunar spacecraft trajectories 3:13 Table of contents 4:31 Circular restricted three-body problem 6:04 Lunar rotating frame 8:18 Equations of motion 10:55 Tisserand relation, Jacobi constant 12:16 Dynamics along Tisserand curves 14:00 Realms of energetically possible motion 15:00 Five energy cases and zero velocity surfaces 18:05 Necks at Lagrange points L1, L2, and L3 18:54 Motion near the stable Lagrange points L4 and L5 22:34 Tadpole and horseshoe orbits 23:45 Oterma comet goes between interior, secondary and exterior realms 25:34 Motion near lunar L1 and L2 29:17 Periodic and quasiperiodic orbits about L1 or L2 34:57 Periodic orbit family metro map 37:21 Stability of trajectories, especially periodic orbits 42:47 Stability of halo orbit 47:12 Quasi-halo orbits around a halo orbit 52:50 MATLAB code description 58:05 MATLAB Demonstration, compute a halo orbit and manifolds 1:04:31 Connections between cislunar and heliocentric space 1:09:16 Mean motion resonances, Lunar gravity assists 1:14:45 Effect of distant lunar flybys, analytical model 1:18:50 Global phase space dynamics, chaotic sea, stable sea shores, stable resonant islands 1:20:00 Resonance zone within the chaotic sea 1:24:40 More realistic models ► Free Book on the 3-Body Problem Dynamical Systems, the Three-Body Problem and Space Mission Design. https://ross.aoe.vt.edu/books ► Teacher Bio 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). ► X / rossdynamicslab ▶️ Next: 3-Body Problem Course • Three Body Problem Introduction: Lecture 1... ▶️ Applications to dynamical astronomy • Interplanetary Transport Network: Mapping ... 📺 Watch my Course Playlists here: • Three-Body Problem Orbital Dynamics • Space Manifolds - Three-Body Problem Orbit... • Space Vehicle Dynamics • Nonlinear Dynamics and Chaos | Online Course • Analytical Dynamics - Lagrangian and 3D Ri... • Advanced Dynamics - Hamiltonian Systems an... • Center Manifolds, Normal Forms, and Bifurc... differential correction single and multiple shooting collocation state transition matrix variational equations #ThreeBodyProblem #EarthMoon #Cislunar #Astrodynamics #OrbitalMechanics