A system of 2n, first order, ordinary differential equations (1) is a Hamiltonian system with n degrees of freedom. (When this system is non-autonomous, it has n+1/2 degrees of freedom.) Here H is the Hamiltonian, a smooth scalar function of the...

In classical mechanics, a Hamiltonian system is a physical system in which forces are velocity invariant. Hamiltonian systems are studied in Hamiltonian mechanics. In mathematics, a Hamiltonian system is a system of differential equations which can be...