Nonstandard Hamiltonian structures of the Liénard equation and contact geometry

The construction of nonstandard Lagrangians and Hamiltonian structures for Liénard equations satisfying Chiellini condition is presented and their connection to time-dependent Hamiltonian formalism is shown. We also show that such nonstandard Lagrangians are deformations of simpler standard Lagrangians. We also exhibit their connection with contact Hamiltonian mechanics.