Constants of motion associated with alternative Hamiltonians

Abstract

It is shown that if a non-autonomous system of $2n$ first-order ordinary differential equations is expressed in the form of the Hamilton equations in terms of two different sets of coordinates, $(q_i,p_i)$ and $(Q_i,P_i)$, then the determinant and the trace of any power of a certain matrix formed by the Poisson brackets of the $Q_i,P_i$ with respect to $q_i,p_i$, are constants of motion.