This book addresses the analytical dynamics of multibody systems and is intended for a one- to two-semester advanced graduate-level course in analytical dynamics. The emphasis is on a solid theoretical foundation with examples that concretely illustrate the theory. I have included a chapter on the fundamental mathematics that is helpful in navigating the principles of dynamics. This includes coverage of linear systems and differential geometry. A chapter on kinematics, the study of the geometry of motion, follows. The first chapter, on dynamics, addresses conservation principles, fundamentally the conservation of momentum embodied in the Newton-Euler Principles. Historically, analytical mechanics (dynamics) has referred to the so-called variational principles, rooted in the calculus of variations. Three chapters cover zeroth-, first-, and second-order variational principles, respectively. Lagrangian and Hamiltonian mechanics are among the more well-known formulations arising from variational principles covered in this book. I also cover important, but lesser known, higher-order principles, including Jourdain's Principle of Virtual Power, Gauss's Principle of Least Constraint, and Hertz's Principle of Least Curvature, as well as Kane's formulation and the Gibbs-Appell formulation.

As an aside, it is worth noting that modern theoretical physics emerged out of the classical variational principles. Einstein's general theory of relativity is commonly formulated using Lagrangian mechanics. Dirac was the first to use the Lagrangian in quantum mechanics and provided separate formulations of quantum mechanics and general relativity based on the Hamiltonian formalism. He also provided a generalized formulation of constrained Hamiltonian systems. Additionally, Feynman's path integral formulation of quantum mechanics has its classical ancestry in Hamilton's Principle of Least Action.

After the chapters on the variational principles, I have included a chapter on an alternate formulation of classical dynamics that has found significant utility in the control of robotic systems. The so-called task space formulation of dynamics was pioneered by Khatib under the name of operational space dynamics. It provides a transformation of the configuration space description of system dynamics into a more convenient task-oriented description. An applications-oriented chapter is included on biomechanical systems. This provides a basic overview of musculoskeletal and neuromuscular biomechanics with extensive coverage of application examples using actual anthropometric and muscle property data. The final chapter provides a brief survey of some analytical dynamics software.