Rigid Body as a Constrained System: Lagrangian and Hamiltonian Formalism

ISBN-13: 9781036412876 / Twarda / 2024

Alexei A. Deriglazov

Opis

This book presents the dynamics of spinning bodies, the most confusing topic in Classical Mechanics, using both Lagrangian and Hamiltonian formulations. Choosing the variational problem as a sole starting point, it treats the rigid body as a system of particles with holonomic constraints within the standard methods of classical mechanics, eliminating the need for additional postulates. All basic quantities, equations, and integrals of motion are derived systematically. The rotation matrix, central to the formalism, is the main focus. The reader should find this approach more simple, transparent, and convincing than the traditional presentations. Chapter 2 covers the theory, while subsequent chapters apply the formalism to motions under external forces. Issues of integrability and many cases of solutions in elementary functions are presented. This book is suitable for undergraduate and graduate students familiar with classical mechanics.