perturbation

Analytical Methods and Perturbation Theory for the Elliptic Restricted Three-Body Problem of Astrodynamics

  • Introduction
  • Theoretical Background
    • Elliptic Restricted Three-Body Problem
      • Physical Description
      • Hamiltonian Dynamics
    • Lagrange Equilibrium Points
    • Jacobi Integral
    • Kolmogrov, Arnold, Moser Theory
      • Integrability and Invariant Tori
      • Resonance and Degeneracy
      • KAM Theorem
  • Canonical Perturbation Theory
    • Motivation
    • Perturbation Theory and Von Zeipel’s Method
  • Dynamical Analysis
    • System Normalization
      • Unperturbed System
    • Stability Analysis
      • Linearized, Non-circular Stability
      • Nonlinear System Stability
  • Conclusions