A new class of transformations preserving Hamilton´s equations

A general condition for the preservation of Hamilton´s equations under coordinate transformation is derived. This preservation condition is exploited to derive a new class of transformations. The existence conditions for such transformations are presented. An example of the application of this approach to a system defined by two generalized coordinates is presented. This approach leads to a restricted set of Hamiltonian systems that admit a linear representation in the transformed coordinates. The drawback of this approach is that the original Hamiltonian is retrieved from a target-Hamiltonian possessing some desirable properties