Some applications of time‐dependent canonical transformations to nonlinear nonconservative classical systems

The recently proposed time‐dependent canonical transformation method of Leach for the quadratic Hamiltonian has been extended to deal with nonlinear nonconservative classical systems. It is observed that the linear time dependent canonical transformations are not adequate to remove the time dependence of any arbitrary time‐dependent nonlinear Hamiltonian. Alternatively, we propose that such a Hamiltonian may be transformed to a quadratic form by means of successive nonlinear canonical transformations. It is also shown that the canonical method is useful to obtain solutions for differential equations governing certain dissipative classical systems.