Question

Time dependent force,obtaining x(t),v(t) in case of integration method.

Answer 1

Explanation:

Abstract

A solution of motion defined by a Hamiltonian function

of a system in time-dependent fields, is found by the use of power series expansions in a perturbation parameter. The solution is in the form of 2N independent integrals of motion, the perturbation terms of the integrals being described by recursion formulas. The integrals of motion are canonically conjugate quantities.

The method is also used to evaluate the distribution function as the general nonlinear solution of the Vlasov equation (in collisionless plasma kinetics, the distribution function as a solution of the Vlasov equation is an integral of motion).