NUMERICAL INTEGRATION OF AN ORBIT AND ITS CONCOMITANT VARIATIONS BY RECURRENT POWER SERIES

Abstract

Power series expansions (with coefficients obtained by recurrence formulas) are more efficient than other integration procedures for computing concurrently an orbit and the resolvent matrix of its variational equations, in the Restricted Problem of Three Bodies. For the same requirements on accuracy, the series expansions use only about 30 per cent of the computing time of the multi-step procedures, and only 12 to 15 per cent of the computing time of the Runge-Kutta-Nystrom method.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1965
Accession Number
AD0628934

Entities

People

  • Andre Deprit
  • R. V. Zahar

Organizations

  • Boeing

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Computations
  • Computers
  • Coordinate Systems
  • Differential Equations
  • Equations
  • Equations Of Motion
  • Errors
  • Hamiltonian Functions
  • Identities
  • Jet Propulsion
  • Numerical Integration
  • Power Series
  • Runge Kutta Method
  • Scientific Research
  • Variational Equations

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematics or Statistics

Technology Areas

  • Space
  • Space - Orbital Debris