An Estimate for the Number of Relative Equilibria in the Motion of a Plane Rigid Body and a Material Point under Mutual Attraction

E.I. Kugushev; V.I. Nikonov

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An Estimate for the Number of Relative Equilibria in the Motion of a Plane Rigid Body and a Material Point under Mutual Attraction

机译：平面刚体与物质点相互吸引作用下相对平衡数的估计。

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The plane motion of a rigid body with a discrete mass distribution and a material point under mutual attraction is considered. The stationary configurations of this mechanical system are studied in the case when the mass of the material point can be ignored and the body rotates about its mass center at a nonzero angular velocity and in the general case of mutual interaction between the body and the material point. It is shown that in this mechanical system there always exist at least two different positions of relative equilibrium.

机译：考虑具有离散质量分布和相互吸引下的材料点的刚体的平面运动。在以下情况下研究该机械系统的静态配置：在忽略物质点的质量并且物体以非零角速度绕其质心旋转的情况下，并且通常情况下，物体与物质点之间存在相互作用。结果表明，在该机械系统中，总是存在至少两个不同的相对平衡位置。

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《Moscow University Mechanics Bulletin》 |2015年第6期|144-148|共5页
作者
E.I. Kugushev; V.I. Nikonov;
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Moscow State University, Faculty of Mechanics and Mathematics, Leninskie Gory, Moscow, 119899, Russia;

Moscow State University, Faculty of Mechanics and Mathematics, Leninskie Gory, Moscow, 119899, Russia;

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2. On a periodic motion of a rigid body carrying a material point in the presence of impacts with a horizontal plane [J] . Markeev A.P. Regular & chaotic dynamics . 2012,第2期

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3. The Implementation of a Given Motion of a Rigid Body Relative to Its Center of Mass by Moving the Material Point [J] . Doklady. Physics . 2019,第11期

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4. On relative equilibria of mutually gravitating massive point and triangular rigid body [C] . Vasily I. Nikonov Symposium of the International Astronomical Union . 2014

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An Estimate for the Number of Relative Equilibria in the Motion of a Plane Rigid Body and a Material Point under Mutual Attraction

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