Nonlinear dynamics of a particle on a rotating parabola via the analytic and semi-analytic approaches

In present study, nonlinear dynamics of a particle on a rotating parabola are analyzed by means of the analytic and semi-analytic approaches. The Energy balance method (EBM), homotopy perturbation method (HPM) and amplitude–frequency formulation (AFF) are applied as the analytic approaches and the frequency-amplitude relationships are obtained. The governing equation of motion is also solved by the differential transform method (DTM) as a semi-analytic approach. The effects of different parameters on the governing equation are evaluated. Comparison of results with exact and numerical solutions are investigated. the performance and capability of each method are revealed and discussed.