This book treats a cluster of classical phenomena: Procession, Euler Angles, Space and Body Coordinates, Coriolis Force, and Foucault's Pendulum. These topics cause students grief because they require depth and clarity in Linear Algebra and nearby topics. The goal here is to present the mathematics with unusual depth and clarity, and then exploit that in an exposition of these parts of Classical Physics.
These topics are often treated in upper division or graduate courses in Classical Mechanics, and are used in Robotics and Celestial Mechanics and other places in Mechanical Engineering.
The book starts with a treatment of Linear Algebra, giving special attention to the parts that physicists and engineers need to understand. Then on to Lie Groups and Lie Algebras, and then a treatment of some Classical Physics at the upper division level. Then the advertised problems are treated.
The book is based on a three-volume set by the same author.