A Third-Order Analytical Solution for Relative Motion with a Circular Reference Orbit

Abstract

From a Lagrangian approach for the development of the relative motion equations for a nonlinear Hill's problem, it is shown that the influence of a spherical primary mass takes the form of a third-body-like disturbing function expressed relative to the origin of Hill's rotating frame. The resulting Lagrangian and corresponding equations of motion are compact and can provide an easily obtainable representation of the nonlinear contributions to the motion to an arbitrary order using recursion relations. The relative equations are expanded through third-order in the local Hill's coordinates and a correspondingly accurate successive approximations solution is developed to describe nonlinear periodic motions in the Hill's frame.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 2002
Accession Number
ADA406244

Entities

People

  • David L. Richardson
  • Jason W. Mitchell

Organizations

  • Air Force Research Laboratory

Tags

Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Air Force
  • Air Force Facilities
  • Air Force Research Laboratories
  • Aircrafts
  • Amplitude
  • Angular Momentum
  • Control Theory
  • Differential Equations
  • Engineering
  • Equations
  • Equations Of Motion
  • Errors
  • Military Research
  • Nonlinear Differential Equations
  • Numerical Integration
  • Relative Motion
  • Vehicles

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)

Technology Areas

  • Space
  • Space - Orbital Debris