引力弹性球同步轨道的渐近稳定性
Asymptotic stability of synchronous orbits for a gravitating elastic sphere
摘要：
我们研究弹性体的动力学，其形状和位置由于点状行星施加的引力而演变。我们在四极近似下工作。我们考虑的解决方案，其中的质心的身体在一个圆形的轨道上移动，并在一个同步的方式旋转的身体围绕其轴，使它总是显示相同的面对行星，因为月球与地球。我们证明了，如果任何内部变形的身体耗散一些能量，那么这样的轨道是局部渐近稳定的。证明是基于适当坐标系的构建和拉萨尔原理的使用。本文主要讨论了弹性体与引力场相互作用的运动学问题。我们认为这本身可能会有一些利益。
英文摘要：
We study the dynamics of an elastic body whose shape and position evolve due to the gravitational forces exerted by a pointlike planet. We work in the quadrupole approximation. We consider the solution in which the center of mass of the body moves on a circular orbit, and the body rotates in a synchronous way about its axis, so that it always shows the same face to the planet as the Moon does with the Earth. We prove that if any internal deformation of the body dissipates some energy, then such an orbit is locally asymptotically stable. The proof is based on the construction of a suitable system of coordinates and on the use of LaSalle's principle. A large part of the paper is devoted to the analysis of the kinematics of an elastic body interacting with a gravitational field. We think this could have some interest in itself.
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