Construction of autonomous canonical systems when the Hamiltonian depends explicitly on time
If the Hamiltonian function of a dynamical system depends explicitly on the time variable, the resulting system of Hamilton's equations is not autonomous. An explicit method of extension is given whereby a new pair of conjugate variables is introduced so that the extended system remains Hamiltonian, but becomes autonomous. The new generalized coordinate turns out to be the instantaneous value of the original Hamiltonian function of the dynamical orbit, while the new conjugate momentum is the old time variable. A fully canonical formalism is obtained, together with a redefined Poisson bracket, a Poisson algebra of smooth functions on the extended phase space, and a Hamilton-Jacobi theory.
scientific article; zbMATH DE number 4041358