Model and Dynamics Analysis of a New Oscillator under Gravity

A mathematical modal for a new oscillator under Gravity is gived by The Second Law of Neton and proved the correctness by The Energy Method .We obtained a equation for the equilibrium point of system by the definition .We observe the dynamics action by the Hamilton function.Meanwhile the phase trajectories and the Poincare sections are also presented. The analysis shows the complicated nonlinear dynamics with periodic motion in some special case.