1306.3737 (Maxim V. Pavlov et al.)

Classical Mechanical Systems with one-and-a-half Degrees of Freedom and
Vlasov Kinetic Equation    [PDF]

Maxim V. Pavlov, Sergey P. Tsarev

We consider non-stationary dynamical systems with one-and-a-half degrees of freedom. We are interested in algorithmic construction of rich classes of Hamilton's equations with the Hamiltonian H=p^2/2+V(x,t) which are Liouville integrable. For this purpose we use the method of hydrodynamic reductions of the corresponding one-dimensional Vlasov kinetic equation. Also we present several examples of such systems with first integrals with non-polynomial dependencies w.r.t. to momentum. The constructed in this paper classes of potential functions {$V(x,t)$} which give integrable systems with one-and-a-half degrees of freedom are parameterized by arbitrary number of constants.

View original: http://arxiv.org/abs/1306.3737