On the geometry of motions in one integrable problem of the rigid body dynamics

JOURNAL OF GEOMETRY AND PHYSICS

卷:87

Article

Kharlamova, I. I.¹  Savushkin, A. Y.¹ 

[1] Russian Acad Natl Econ & Publ Adm, Volgograd Branch, Volgograd, Russia

关键词: Rigid body;    Hodograph method;    Partial motions;    Decomposition;   

DOI  :  10.1016/j.geomphys.2014.07.010

来源: Elsevier

【 摘 要 】

Due to Poinsot's theorem, the motion of a rigid body about a fixed point is represented as rolling without slipping of the moving hodograph of the angular velocity over the fixed one. If the moving hodograph is a closed curve, visualization of motion is obtained by the method of P.V. Kharlamov. For an arbitrary motion in an integrable problem with an axially symmetric force field the moving hodograph densely fills some two-dimensional surface and the fixed one fills a three-dimensional surface. In this paper, we consider the irreducible integrable case in which both hodographs are two-frequency curves. We obtain the equations of bearing surfaces, illustrate the main types of these surfaces. We propose a method of the so-called non-straight geometric interpretation representing the motion of a body as a superposition of two periodic motions. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

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