Accession Number:

AD0645478

Title:

NATURAL FAMILIES OF PERIODIC ORBITS

Descriptive Note:

Corporate Author:

BOEING SCIENTIFIC RESEARCH LABS SEATTLE WA MATHEMATICS RESEARCH LAB

Personal Author(s):

• Deprit, Andre
• Henrard, Jacques

Report Date:

1966-10-01

Pagination or Media Count:

56.0

Abstract:

In reference to any solution of a conservative dynamical system with two degrees of freedom, Hills 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.

Descriptors:

• *CELESTIAL MECHANICS
• *NUMERICAL ANALYSIS
• ALGORITHMS
• ANALYTIC FUNCTIONS
• CALCULUS OF VARIATIONS
• CORRECTIONS
• EQUATIONS OF MOTION
• TOPOLOGY

Subject Categories:

• Celestial Mechanics
• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE