Accession Number : AD0716776

Title :   Introduction to Resonance Problems,

Corporate Author : TEXAS UNIV AUSTIN APPLIED MECHANICS RESEARCH LAB

Personal Author(s) : Giacaglia,G. E. O.

Report Date : AUG 1970

Pagination or Media Count : 32

Abstract : Consider a Dynamical System defined by a Hamiltonian Function H(q,p), where q and p are n-vectors in phase space (q,p). For simplicity, H is supposed to be analytic in a certain region R. The equations of motion are q dot = H sub p, p dot = (-H sub q). One also admits the existence of an isolated stationary solution in R, corresponding to the point (q sup 0, p sup 0), that is H sub p0 = 0 = H sub q0 while the Hessian determinant is supposed not to be zero. The problem of motion in the vicinity of (q sup 0, p sup 0) can be reduced to a problem of perturbation of a linear system and its solution depends essentially on the relations among the frequencies of the linear system. These frequencies are actually the normal modes of the system when infinitely close to the stationary solution. (Author)

Descriptors :   (*N-BODY PROBLEM, EQUATIONS OF MOTION), (*PERTURBATION THEORY, RESONANCE), SET THEORY, TRANSFORMATIONS(MATHEMATICS), TAYLOR'S SERIES, APPROXIMATION(MATHEMATICS), LINEAR SYSTEMS, ANALYTIC FUNCTIONS, HAMILTONIAN, TOPOLOGY, THEOREMS

Subject Categories : Celestial Mechanics
      Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE