Finite Dimensional Isochronous Nonlinear Oscillating Systems

This book presents a study of isochronous properties associated with certain classes of Liénard type of equations including linear Liénard type equation, quadratic Liénard type equation, mixed quadratic linear Liénard type equation and their higher order generalizations and identified the equations belonging to above mentioned equations exhibiting isochronous properties. The major issues considered in this book is to develop a systematic procedure for to identify the collective coordinate which is conjugate to the given Hamiltonian in order to generate isochronous systems. By generalizing this procedure for coupled systems in terms of ¿i modified Hamiltonians and identified suitable canonically conjugate coordinates such that the constructed ¿i modified Hamiltonian is nonsingular and the corresponding Newton's equation of motion is constraint free. Further, a class of N-coupled mixed quadratic linear Liénard type equations can also be identified with the help of a specific nonlocal transformation that possesses isochronous properties and studied their integrability properties.