Exact invariants for a class of three-dimensional time-dependent classical hamiltonians
An exact invariant is derived for three-dimensional Hamiltonian systems of N particles confined within a general velocity-independent potential. The invariant is found to contain a time-dependent function f(2)(t), embodying a solution of a third-order differential equation whose coefficients depend on the explicitly known trajectories of the particle ensemble. Our result is applied to a one-dimensional time-dependent nonlinear oscillator and to a system of Coulomb interacting particles in a time-dependent quadratic external potential.
Struckmeier
J
Gesellschaft fur Schwerionenforschung (GSI), Planckstrasse 1, 64291 Darmstadt, Germany.
Riedel
C