CHIELLINI INTEGRABILITY CONDITION, PLANAR ISOCHRONOUS SYSTEMS AND HAMILTONIAN STRUCTURES OF LIENARD EQUATIONPartha Guha$2

摘要

Using a novel transformation involving the Jacobi Last Multiplier (JLM) we derive an old integrability criterion due to Chiellini for the Lienard equation. By combining the Chiellini condition for integrability and Jacobi's Last Multiplier the Lagrangian and Hamiltonian of the Lienard equation is derived. We also show that the Kukles equation is the only equation in the Lienard family which satisfies both the Chiellini integrability and the Sabatini criterion for isochronicity conditions. In addition we examine this result by mapping the Lienard equation to a harmonic oscillator equation using tacitly Chiellini's condition. Finally we provide a metriplectic and complex Hamiltonian formulation of the Lienard equation through the use of Chiellini condition for integrability.