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The primary reason for writing the book was to give an account of the subject which was firmly rounded in both the classical and geometrical foundations of the subject. The book is intended to be accessible to a student who is well prepared in linear algebra and advanced calculus, who has had an introductory course in mechanics and who has a certain degree of mathematical maturity. Any mathematics needed beyond this is included in the text.
Chapter 1 deals with the rotations, the basic operation in rigid body theory. Rotations are presented in several parameterizations including axis angle, Euler angle, quaternion, and Clayey-Klein parameters. The rotations form a e group which underlies all of rigid body mechanics. Chapter 2 studies rigid body motions, angular velocity, and the physical concepts of angular momentum and kinetic energy. The fundamental idea of angular velocity is straight from the Lie algebra theory.
These concepts are illustrated with several examples from physics and engineering. Chapter 3 studies rigid body dynamics in vector, Lagging, and Hamiltonian formulations. This chapter introduces many geometric concepts as dynamics occurs on differential manifolds and for rigid body mechanics the manifold is often a Lie group. The idea of the adjoins action is seen to be basic to the rigid body equations of motion. This chapter contains many examples from physics and engineering.
Chapter 4 considers the dynamics of constrained systems. Here Lagrange multipliers are introduced and several ways of determining or eliminating them are considered. This topic is rich in geometrical interactions and there are several examples, some standard and some not. Chapter 5 considers the intolerable problems of free rotation, Leganes’s top, and the cryostat. The Kowalski top and Lax equations are also considered.