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