perturbation

A Perturbation Theory for Hamilton’s Principal Function: Applications to Boundary Value Problems

  • Introduction
  • Hamiltonian Dynamics
  • Perturbation Theory for Hamilton’s Principal Function
  • Perturbation Theory for the Two-Point Boundary Value Problem .
  • Perturbation Theory for the Initial Value Problem
  • Perturbed Rotating Two-Body Problem
  • Example: Solving the Perturbed Two-Body Two-Point Boundary Value Problem
    • Hamilton’s Principal Function for the Two-Body Problem
      • Energy Constraint
    • Perturbation Theory for the Two-Body Problem Hamilton’s Principal Function
    • Implementation of Perturbation Theory to Numerical Simulations
    • Perturbation Theory for the Hohmann Transfer
    • Perturbation Theory for Lambert’s Problem
    • Contour Map for the Nominal Two-Point Boundary Value Problem
    • Implementation of Perturbation Theory to Perturbed Contour Map
      • Numerical Errors in LEO to GEO Transfer
      • Example: Perturbed LEO to GEO Hohmann Transfer
      • Physical Explanation of Perturbed Contour Map Results
  • Example: Solving the Perturbed Two-Body Initial Value Problem
    • Perturbation Theory for the Two-Body Problem Hamilton’s Principal and Characteristic Functions
      • First-Order Perturbation Theory for the Two-Body Initial Value Problem
    • Implementation of the First-Order Perturbation Theory to Numerical Simulations
      • Application of the Perturbation Theory to the Restricted Three-Body Problem
    • Numerical Example: Planar Perturbed Two-Body Problem
      • Numerical Example: Non-Planar Perturbed Two-Body Problem
    • Application of the First-Order Perturbation Theory to the Perturbed Restricted Three-Body Problem
    • Interpretation of Numerical Results from Perturbation Theory