The equations of motion for a dynamically symmetric n-dimensional fixed rigid body-pendulum situated in a rioricoriservative force field are studied. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of an incident medium. The complete list of transcendental first integrals expressed in terms of finite combinations of elementary functions is found.

中文翻译：

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耗散在多维球面正切束上的可积系统的新情况

研究了一个位于动静力场中的动态对称n维固定刚体摆的运动方程。这些方程式的形式取自放置在均匀入射介质流中的实际固定刚体的动力学。找到了以基本函数的有限组合表示的先验第一积分的完整列表。