Accession Number:

AD0647194

Title:

BIRKHOFF NORMALIZATION PROCESS PROGRAM FOR TIME-INDEPENDENT HAMILTONIAN SYSTEMS,

Descriptive Note:

Corporate Author:

GENERAL PRECISION INC LITTLE FALLS N J AEROSPACE RESEARCH CENTER

Personal Author(s):

• Chai,Winchung A.
• Kass,Sheldon

Report Date:

1966-10-01

Pagination or Media Count:

48.0

Abstract:

This is a complete documentation program description of a computer package for analyzing finite time stability properties of equilibrium points of time-independent Hamiltonian systems. Using this package, approximate analytic solutions which contain nonlinear effects can be constructed near these equilibrium points. Three main programs constitute the complete package. The first program normalizes and computes the generating functions for a time-independent Hamiltonian in the neighborhood of an equilibrium point, the second expresses coordinate transformations as truncated power series, and the third program computes point-by-point coordinate transformations. To demonstrate the procedure, the report describes in detail the application of the computer package to the construction of solutions of the planar restricted three-body problem near the L4 equilibrium point. Numerical results compare very favorably in precision with values obtained by numerical integration. The computer time required for the entire normalization process is only a small fraction of the integration time, however. Author

Descriptors:

• *COMPUTER PROGRAMS
• *HAMILTONIAN FUNCTIONS
• *CELESTIAL MECHANICS
• *N BODY PROBLEM
• DIGITAL COMPUTERS
• NUMERICAL INTEGRATION
• EQUATIONS OF MOTION

Subject Categories:

• Celestial Mechanics
• Numerical Mathematics
• Computer Programming and Software
• Computer Hardware

Distribution Statement:

APPROVED FOR PUBLIC RELEASE