NATURAL FAMILIES OF PERIODIC ORBITS

Abstract

In reference to any solution of a conservative dynamical system with two degrees of freedom, Hill's equation is generalized to encompass non- necessarily isoenergetic displacements as well as the isoenergetic displacements caused by a variation of a parameter. This new variational equation is made the foundation of a methodical procedure for continuing numerically natural families of periodic orbits. The method consists of two steps-- an isoenergetic corrector and a tangential predictor. Although the algorithm makes no assumption of symmetry on the periodic orbits to be continued, special attention is paid to the symmetric orbits, but only to show how in these cases the method can be simplified substantially.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1966
Accession Number
AD0645478

Entities

People

  • Andre Deprit
  • Jacques Henrard

Organizations

  • Boeing

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Analytic Functions
  • Cartesian Coordinates
  • Celestial Mechanics
  • Computational Science
  • Computations
  • Differential Equations
  • Equations
  • Equations Of Motion
  • Formulas (Mathematics)
  • Hamiltonian Functions
  • Identities
  • Integrals
  • Linear Differential Equations
  • Numbers
  • Periodic Functions
  • Power Series
  • Variational Equations

Readers

  • Space Exploration and Orbital Mechanics.
  • Structural Dynamics.
  • Systems Analysis and Design

Technology Areas

  • Space
  • Space - Orbital Debris