A direct approach to finding exact invariants for one‐dimensional time‐dependent classical Hamiltonians

@inproceedings{Lewis1982ADA,
  title={A direct approach to finding exact invariants for one‐dimensional time‐dependent classical Hamiltonians},
  author={Henry R. Lewis and P. G. L. Leach},
  year={1982}
}
For a classical Hamiltonian H=(1/2) p2+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)=∑∞n=0pnfn(q,t), are examined. The method is based on direct use of the equation dI/dt=∂I/∂t +[I,H] =0. A recursion relation for the coefficients fn(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… CONTINUE READING

Citations

Publications citing this paper.
SHOWING 1-10 OF 18 CITATIONS