Canonical transformations are defined by their ability to preserve Hamilton's equations in classical mechanics. This preservation is crucial because it ensures that the physical laws governing a system remain invariant under the transformation. Non-canonical transformations fail to maintain this invariance, leading to discrepancies in the equations of motion. Therefore, any transformation of coordinates that successfully preserves Hamilton's equations qualifies as a canonical transformation.
PREREQUISITESPhysicists, students of classical mechanics, and anyone interested in advanced topics in Hamiltonian dynamics.