Direct approach to finding exact invariants for one-dimensional time-dependent classical Hamiltonians

Journal Article · Wed Dec 01 04:00:00 EST 1982 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.525329· OSTI ID:6898371

Lewis, H R; Leach, P G.L.

For a classical Hamiltonian H = (1/2) p/sup 2/+V(q,t) with an arbitrary time-dependent potential V(q,t), exact invariants that can be expressed as series in positive powers of p, I(q,p,t) = summation/sup infinity//sub n/ = 0p/sup n/f/sub n/(q,t), are examined. The method is based on direct use of the equation dI/dt = partialI/partialt +(I,H) = 0. A recursion relation for the coefficients f/sub n/(q,t) is obtained. All potentials that admit an invariant quadratic in p are found and, for those potentials, all invariants quadratic in p are determined. The feasibility of extending the analysis to find invariants that are polynomials in p of higher degree than quadratic is discussed. The systems for which invariants quadratic in p have been found are transformed to autonomous systems by a canonical transformation.

• Research Organization: Los Alamos National Laboratory, Los Alamos, New Mexico 87545
• OSTI ID: 6898371
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 23:12; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CLASSICAL MECHANICS
FUNCTIONS
HAMILTONIANS
INVARIANCE PRINCIPLES
MATHEMATICAL OPERATORS
MECHANICS
ONE-DIMENSIONAL CALCULATIONS
POLYNOMIALS
POTENTIALS
QUANTUM OPERATORS
RECURSION RELATIONS
TIME DEPENDENCE