引用本文: 谢建华. 球形浮体全局动力学方程. 力学与实践, xxxx, x(x): 1-8.
Xie Jianhua. The global dynamical equation of spherical floating body. Mechanics in Engineering, xxxx, x(x): 1-8.
 Citation: Xie Jianhua. The global dynamical equation of spherical floating body. Mechanics in Engineering, xxxx, x(x): 1-8.

## THE GLOBAL DYNAMICAL EQUATION OF SPHERICAL FLOATING BODY

• 摘要: 本文首先通过变上限积分公式，得到了浮体恢复力的公式，给出了浮体有限振动方程；通过线性化方法，获得了浮体在平位置附近小振动频率公式；然后考虑浸没、漂浮和飞行阶段，建立了球形浮体分段光滑的全局动力学方程，用相平面方法描述了其全局动力学。 其次考虑了具有一个空腔的球形浮体上下沉浮和左右晃动的耦合振动问题；给出了浮力、浮力矩以及势能函数表达式，建立了球形浮体的两自由度动力学方程。结果表明在稳定平衡位置附近，上下沉浮和左右晃动过程是非耦合的，因此可以单独考虑某一方向振动和稳定性问题。系统的两个平衡位置可能导致复杂运动的产生。

Abstract: 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.

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