Accession Number : AD0683023

Title :   ON PERIODICALLY PERTURBED CONSERVATIVE SYSTEMS,

Corporate Author : CALIFORNIA UNIV LOS ANGELES NUMERICAL ANALYSIS RESEARCH

Personal Author(s) : Lazer,A. C. ; Sanchez,D. A.

Report Date : 1967

Pagination or Media Count : 14

Abstract : The main result of this paper is concerned with the differential equation (1) the second derivative of x with respect to t + grad G(x) = p(t) where p epsilon C(R,R superscript n) and is 2 pi-periodic, and G epsilon C superscript 2 (R superscript n,R). The equation (1) can be interpreted physically as the Newtonian equations of motion of a mechanical system subject to conservative internal forces and periodic external forces. Specifically it is shown that under certain conditions, equation (1) has a 2 pi periodic solution.

Descriptors :   (*FUNCTIONAL ANALYSIS, DIFFERENTIAL EQUATIONS), (*DIFFERENTIAL EQUATIONS, PERIODIC VARIATIONS), EQUATIONS OF MOTION, BOUNDARY VALUE PROBLEMS, HILBERT SPACE, INTEGRAL EQUATIONS, MATRICES(MATHEMATICS), FOURIER ANALYSIS, INEQUALITIES, SERIES(MATHEMATICS), THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE