THE COMPUTATION OF CHARACTERISTIC EXPONENTS IN THE PLANAR RESTRICTED PROBLEM OF THREE BODIES

Abstract

The canonical equations of motion in barycentric synodical Cartesian coordinates and momenta are integrable by means of recurrent power series; these series are proved to be convergent for initial conditions anywhere in the phase space except in the two phase planes of binary collisions. The integration by recurrent power series is extended to the variation equations. It is used to compute the monodromy matrix associated to the fundamental period of a periodic orbit. A simple formula is derived, which relates the trace of the monodromy matrix and the characteristic exponents. These numerical methods are applied to evaluate the characteristic exponents of Rabe's Trojan Orbits; they are found to be of the stable type for the ovals, and of the unstable type for the horse-shoe shaped orbit. When the periodic orbit is symmetric with respect to the axis of syzygies, four independent variational solutions computed only over half the period are shown to be sufficient for evaluating the characteristic exponents.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1965
Accession Number
AD0622985

Entities

People

  • Andre Deprit
  • J. F. Price

Organizations

  • Boeing

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies
  • Space

DTIC Thesaurus Topics

  • Accuracy
  • Cartesian Coordinates
  • Coefficients
  • Computations
  • Computer Programming
  • Computer Programs
  • Computers
  • Coordinate Systems
  • Differential Equations
  • Equations
  • Equations Of Motion
  • Hamiltonian Functions
  • Identities
  • Inequalities
  • Power Series
  • Procedures (Computers)
  • Variational Equations

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Combustion and Flow Dynamics.
  • Space Exploration and Orbital Mechanics.

Technology Areas

  • Space
  • Space - Orbital Debris