Explore the complexities of orbital dynamics in cislunar space through this comprehensive lecture on the restricted 3-body model. Delve into the fundamentals of astrodynamics beyond the geosynchronous belt, covering topics such as lunar mean motion resonances, libration-point orbits, and invariant manifolds. Learn about the Lagrange points, various types of orbits including Lissajous and halo orbits, and the stability of periodic orbits. Gain insights into the application of MATLAB for differential correction and modeling. Discover the connections between cislunar and heliocentric space, orbital resonances, and the implications for space mission design. Enhance your understanding of advanced concepts in celestial mechanics and their practical applications in space exploration.
Cislunar Space - 3-Body Model of Orbital Dynamics Beyond the Geosynchronous Belt
Overview
Syllabus
Introductory comments
Outline
Equations of motion
3-body energy - constant of motion
Tisserand relation, Tisserand curve meaning
Realms of possible motion
Zero velocity curves
Zero velocity surfaces
Lagrange points
L4, L5 - triangular points
L4, L5 - tadpole and horseshoe orbits
L1, L2 - collinear points
L1, L2 - 4 types of trajectories
Lissajous orbits
Halo orbits 3D
Lyapunov orbits planar
Stability of periodic orbits
Stability of halo orbits
Approaching and departing directions
Quasi-halo orbits
Stable and unstable manifolds
Transition tubes
MATLAB exercise intro
Differential correction
MATLAB demo
Cislunar-heliocentric space connection
Lunar L1 to Sun-Earth L2
Apollo 12 upper stage
Orbital resonance
Resonances with moon
Poincare section
Mixed phase space, chaotic and resonance regions
Semi-analytical model of multiple lunar flybys
Connection with ballistic capture
Persistence in realistic models
References
Taught by
Ross Dynamics Lab
