THE GLOBAL DYNAMICAL EQUATION OF SPHERICAL FLOATING BODY

Firstly, through the formula of variable upper limit integral, the expression for the restoring force of the floating body is obtained, and the finite vibration equation of the floating body is given. By the linearization method, the frequency for small vibration of the floating body around the equilibrium is obtained. Then, considering the immersion, floating and flight stages of the floating body, a piecewise smooth global dynamic equation for the spherical floating body is established, and its global dynamics is described by the phase plane method. Secondly, the coupled vibration problem of the up and down heaving and left and right shaking of a spherical floating body with a cavity is considered. The expressions of buoyancy, buoyancy moment and potential energy function are given, and the dynamical equation of the spherical floating body with two degree of freedom is established. The results show that in the small vibration around the stable equilibrium, the heaving and the shaking processes are uncoupled, so the problems of vibration and stability in a certain direction can be investigated separately. Due to the existence of two equilibrium points, it may lead to appearing of complicated motions.