Generalization of the senator-bapat method to systems having limit cycles

  title={Generalization of the senator-bapat method to systems having limit cycles},
  author={E. Mickens},
  journal={Journal of Sound and Vibration},
  • E. Mickens
  • Published 1999
  • Mathematics
  • Journal of Sound and Vibration
On the Analytical Approximation of the Nonlinear Cubic Oscillator by an Iteration Method
A modified approximate analytic solution of the cubic nonlinear oscillator “ ” has been obtained based on an iteration procedure. Here we have used the truncated Fourier series in each iterativeExpand
Perturbation method for periodic solutions of nonlinear jerk equations
Abstract A Lindstedt–Poincare type perturbation method with bookkeeping parameters is presented for determining accurate analytical approximate periodic solutions of some third-order (jerk)Expand
A generalized iteration procedure for calculating approximations to periodic solutions of “truly nonlinear oscillators”
Abstract An extended iteration method for calculating the periodic solutions of nonlinear oscillator equations is given. The procedure is illustrated by applying it to two “truly nonlinearExpand


Oscillations in Planar Dynamic Systems
  • R. Mickens
  • Computer Science, Mathematics
  • Series on Advances in Mathematics for Applied Sciences
  • 1996
Oscillatory systems harmonic balance Lindstedt-Poincare perturbation methods method of Krylov-Bogoliubov-Mitropolsky general second-order systems numerical techniques. Appendices: mathematicalExpand
A Perturbation Technique that Works Even When the Non-Linearity is Not Small
Abstract We extend the Lindstedt-Poincare small non-linearity based perturbation scheme to strongly non-linear systems. The extended technique starts from a physically non-existent neighboring linearExpand
Bounds on the Fourier coefficients for the periodic solutions of non-linear oscillator equations
The differential equations describing nonlinear oscillations (as seen in mechanical vibrations, electronic oscillators, chemical and biochemical reactions, acoustic systems, stellar pulsations, etc.)Expand
A generalization of the method of harmonic balance
A procedure is provided for generalizing the method of harmonic balance to obtain higher-order approximations to the periodic solutions of differential equations for two systems, one a conservativeExpand
Construction of approximate analytical solutions to a new class of non-linear oscillator equation
The principle of harmonic balance is invoked in the development of an approximate analytic model for a class of nonlinear oscillators typified by a mass attached to a stretched wire. By assuming thatExpand