Classical Dynamics

A Modern Perspective

Classical dynamics is traditionally treated as an early stage in the development of physics, a stage that has long been superseded by more ambitious theories. Here, in this book, classical dynamics is treated as a subject on its own as well as a research frontier. Incorporating insights gained over the past several decades, the essential principles of classical dynamics are presented, while demonstrating that a number of key results originally considered only in the context of quantum theory and particle physics, have their foundations in classical dynamics.

Graduate students in physics and practicing physicists will welcome the present approach to classical dynamics that encompasses systems of particles, free and interacting fields, and coupled systems. Lie groups and Lie algebras are incorporated at a basic level and are used in describing space-time symmetry groups. There is an extensive discussion on constrained systems, Dirac brackets and their geometrical interpretation. The Lie-algebraic description of dynamical systems is discussed in detail, and Poisson brackets are developed as a realization of Lie brackets. Other topics include treatments of classical spin, elementary relativistic systems in the classical context, irreducible realizations of the Galileo and Poincaré groups, and hydrodynamics as a Galilean field theory. Students will also find that this approach that deals with problems of manifest covariance, the no-interaction theorem in Hamiltonian mechanics and the structure of action-at-a-distance theories provides all the essential preparatory groundwork for a passage to quantum field theory.

This reprinting of the original text published in 1974 is a testimony to the vitality of the contents that has remained relevant over nearly half a century.

Contents:

• Introduction: Newtonian Mechanics
• Generalized Coordinates and Lagrange's Equations
• The Hamilton and Weiss Variational Principles and the Hamilton Equations of Motion
• The Relation Between the Lagrangian and the Hamilton Descriptions
• Invariance Properties of the Lagrangian & Hamiltonian Descriptions, Poisson and Lagrange Brackets, and Canonical Transformations
• Group Properties and Methods of Constructing Canonical Transformations
• Invariant Measures in Phase Space and Various Forms of Development in Time
• Theory of Systems with Constraints
• The Generalized Poisson Bracket and Its Applications
• Dynamical Systems with Infinitely Many Degrees of Freedom and Theory of Fields
• Linear and Angular Momentum Dynamical Variables and Their Significance
• Sets, Topological Spaces, Groups
• Lie Groups and Lie Algebras
• Realizations of Lie Groups and Lie Algebras
• Some Important Lie Groups and Their Lie Algebras
• Relativistic Symmetry in the Hamiltonian Formalism
• The Three-Dimensional Rotation Group
• The Three-Dimensional Euclidean Group
• The Galilei Group
• The Poincaré Group
• Manifest Covariance in Hamiltonian Mechanics
• Relativistic Action-at-a-Distance Theories
• Conclusion
• Index

Readership: Graduate students and researchers in classical mechanics and mathematical physics.