On Small Period, Large Amplitude Normal Modes of Natural Hamiltonian Systems.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1984
- Accession Number
- ADA139314
Entities
People
- E. W. C. Van Groesen
Organizations
- University of Wisconsin–Madison