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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...
In this paper, we obtain the approximate solutions for optimal control of linear systems, which have a quadratic performance index. The differential transform method (DTM) is applied for solving the extreme conditions obtained from the Pontryagin’s maximum principle. The differential transform method is one of the approximate methods, which can be easily applied to many linear and nonlinear problems...
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