Accession Number : ADA139314

Title :   On Small Period, Large Amplitude Normal Modes of Natural Hamiltonian Systems.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Groesen,E W C van

PDF Url : ADA139314

Report Date : Jan 1984

Pagination or Media Count : 25

Abstract : Periodic solutions are investigated of the set of second order Hamiltonian equations -x = V'(x) for x(t) e R sub N, where the function V is even, has a certain monotonic behaviour on rays through the origin in R sub N and has superquadratic growth at infinity. It is proven that for T 0 less than the smallest period of the linearized system (if non-trivial, else for all T), there exists a periodic solution of a special kind, a normal mode, which has minimal period T, has large amplitude (tending to infinity as T approaches limit of 0) and which minimizes the action functional on a naturally constrained set. If V has a direction of maximum increase this solution will be characterized completed. A condition for V is given, which is the same as in a multiplicity result for the prescribed energy case, that provides the existence of at least N distinct normal modes of minimal period T. (Author)

Descriptors :   *Hamiltonian functions, *Periodic functions, *Solutions(General), Equations, Amplitude, Linearity, Variational methods, Vector analysis, Kinetic energy, Potential energy

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE