Determination of periodic solutions for the motion of a particle on a rotating parabola by means of the optimal homotopy asymptotic method

This paper deals with the nonlinear oscillations of a particle which moves on a rotating parabola. An analytic approximate technique, namely optimal homotopy asymptotic method (OHAM) is employed to propose an analytic approach to solve nonlinear oscillations. The validity of the OHAM is independent on whether or not there exist small or large parameters in the considered nonlinear equations. Our procedure provides us with a convenient way to optimally control the convergence of the approximate solutions. An example is given and the results reveal that this procedure is very effective, simple and accurate. This paper demonstrates the general validity and the great potential of the OHAM.