×

Classical problems of the dynamics of a rigid body. (Классические задачи динамики твердого тела.) (Russian) Zbl 1284.70002

Zadachi i Metody. Matematika, Mekhanika, Kibernetika 7. Kyïv: Naukova Dumka (ISBN 978-966-001307-0). 402 P. (2012).
Publisher’s description (translated from the Russian): In this seventh volume in the series ‘Problems and methods. Mathematics. Mechanics. Cybernetics’, the authors investigate mathematical problems of the dynamics of a rigid body. They survey the present state of the Euler problem of the motion of a heavy rigid body about a fixed point, present mathematical methods for the analytical and qualitative investigation of the dynamics of a rigid body, and describe important results in the investigation of some interrelated problems of analytical mechanics, such as the reduction of the order of a system of differential equations, the determination of particular solutions and integrable cases by the method of invariant relations, the study of the qualitative properties of motion, the development of Poinsot’s results relating to the kinematic interpretation of motion by the hodograph method, and the application of this method to the investigation of known particular solutions of the dynamics of a rigid body. One of the main aims of this work is to demonstrate the effectiveness of geometric methods for studying the motions of mechanical systems.
This book is intended for researchers and undergraduate and graduate students interested in classical and modern problems of the dynamics of a rigid body.

MSC:

70-02 Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems
70E15 Free motion of a rigid body
70E20 Perturbation methods for rigid body dynamics
PDFBibTeX XMLCite
Full Text: Link