Phys. Rev. Lett. 85, 3830–3833 (2000)Exact Invariants for a Class of Three-Dimensional Time-Dependent Classical HamiltoniansReceived 26 April 2000; revised 8 June 2000; published in the issue dated 30 October 2000 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 f2(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. © 2000 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.85.3830
DOI:
10.1103/PhysRevLett.85.3830
PACS:
41.85.-p, 45.50.Jf
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