Nonlinear generalization of the Floquet theorem and an adiabatical theorem for dynamical systems with Hamiltonian periodic in time
The aim of this paper is to extend the theory of adiabatical invariance to classical Hamiltonian systems with time-periodic potentials or constraints. Such a generalization has been already performed in quantum mechanics (and later on extensively applied, namely in statistical mechanics) but it was based on the Floquet theorem, i.e., use was made of the linearity of the field equations. We show, in the present paper that the main idea of the Floquet theorem can be expressed in a non-linear way. We then introduce in analytical dynamics a new concept called canonical reducibility, which is a non-linear extension of Floquet theorem and we provide a theorem asserting that a dynamical periodic system which is canonically reducible to a conservative and integrable one possesses adiabatical invariants.
- Research Organization:
- Fondation Louis De Broglie, Paris, France
- OSTI ID:
- 6935418
- Report Number(s):
- CONF-8008162-
- Journal Information:
- Hadronic J.; (United States), Vol. 4:3; Conference: 3. workshop on Lie-admissible formulations, Boston, MA, USA, 4 Aug 1980
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
CLASSICAL MECHANICS
HAMILTONIANS
FLOQUET FUNCTION
NONLINEAR PROBLEMS
ADIABATIC INVARIANCE
INVARIANCE PRINCIPLES
QUANTUM MECHANICS
TIME DEPENDENCE
FUNCTIONS
MATHEMATICAL OPERATORS
MECHANICS
QUANTUM OPERATORS
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics