Asymptotic stability and associated problems of dynamics of falling rigid body
Asymptotic stability and associated problems of dynamics of falling rigid body
复制标题
落体刚体动力学的渐近稳定性及相关问题
DOI：
10.1134/s1560354707050061
复制
发表时间：
2007
影响因子：
1.4
通讯作者：
I. Mamaev
中科院分区：
文献类型：
--
作者：
A. Borisov;V. Kozlov;I. Mamaev
我们从刚体动力学的角度考虑了两个问题，并使用新的稳定性和渐近行为分析方法来求解。第一个问题涉及刚体在无限体积的零涡度理想流体中的运动。第二个问题具有类似的渐近行为，涉及雪橇在斜面上的运动。第二个问题的运动方程是非完整的，并且表现出一些哈密顿系统不典型的新特征。对文献进行了全面的综述，并提出了与流体中重体下落运动有关的新问题。
We consider two problems from the rigid body dynamics and use new methods of stability and asymptotic behavior analysis for their solution. The first problem deals with motion of a rigid body in an unbounded volume of ideal fluid with zero vorticity. The second problem, having similar asymptotic behavior, is concerned with motion of a sleigh on an inclined plane. The equations of motion for the second problem are non-holonomic and exhibit some new features not typical for Hamiltonian systems. A comprehensive survey of references is given and new problems connected with falling motion of heavy bodies in fluid are proposed.