Classical Dynamics: A Modern Perspective

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 Poincare Group; Manifest Covariance in Hamiltonian Mechanics; Relativistic Action-at-a-Distance Theories; Conclusion; Index;

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• Mecânica clássica

Classical Dynamics, Group Theory and Dynamics, Spacetime Symmetry Groups