Rigid Body Dynamics

This monograph provides a complete and up-to-date examination of rigid body dynamics using a Lagrangian approach. All known integrable cases, which were previously scattered throughout the literature, are collected here for convenient reference. Also contained are particular solutions to diverse problems treated within rigid body dynamics.

The first seven chapters introduce the elementary dynamics of the rigid body and its main problems. A full historical account of the discovery and development of each of the integrable cases is included as well. Instructors will find this portion of the book well-suited for an undergraduate course, having been formulated by the author in the classroom over many years. The second part includes more advanced topics and some of the author's original research, highlighting several unique methods he developed that have led to significant results. Some of the specific topics covered include the twelve known solutions of the equations of motion in the classical problem, which has not previously appeared in English before; a collection of completely new integrable cases; and the motion of a rigid body around a fixed point under the action of an asymmetric combination of potential and gyroscopic forces. Rigid Body Dynamics will appeal to researchers in the area as well as those studying dynamical and integrable systems theory.

Offers a state-of-the-art overview of rigid body dynamics, covering the fundamentals as well as advances in research Collects all known integrable cases in one convenient volume, which were previously scattered throughout the literature Presents for the first time in English all twelve known solutions of the equations of motion in the classical problem

Résumé
"This book is intended to be a reference book for integrable cases and exact solutions. It can be useful to readers of different mathematical backgrounds: students, mathematicians, physicists or engineers." (Liviu Popescu, zbMATH 1505.70001, 2023)

Contenu
Introduction.- Part 1. Overview of Rigid Body Dynamics.- Distribution of mass.- Description of rotation of a rigid body about a fixed point.- The classical problem: The motion of a heavy rigid body about a fixed point.- General and conditional integrable cases of the classical problem.- The motion of a heavy gyrostat.- Motion of rigid body about a fixed point in the field of a distant Newtonian centre and Brun's problem.- The motion of a body with no fixed point.- Part 2. Research on Rigid Body Dynamics.- Particular solutions of the classical problem and its generalizations.- The rigid body in a potential field.- The problem of motion of a body in a liquid.- The general problem of motion of a rigid body acted upon by a coaxial combination of potential and gyroscopic forces.- The most general integrable in rigid body dynamics.- Miscellaneous cases integrable on a single level of the areas integral.- The rigid body acted upon by a skew combination of fields. <p