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Full Description
Classical Dynamics of Linear and Nonlinear Systems offers a comprehensive exploration of dynamical systems from fundamental principles to advanced applications. This textbook presents a unified treatment of classical dynamics, bridging the gap between linear and nonlinear systems while providing both theoretical foundations and practical applications.
Beginning with a thoughtful classification of dynamical systems, the book systematically builds understanding from particle mechanics to quantum field theory. Following a rigorous analysis of particle dynamics in both configuration and phase spaces (Newtonian, Lagrangian, Hamiltonian and Hamilton-Jacobi formulations), the book provides a detailed examination of molecular and crystalline structures across multiple dimensions. Later chapters conduct an in-depth exploration of nonlinear phenomena and chaos theory with real-world applications and elegant formulations of classical field theories using Lagrangian and Hamiltonian approaches. The final sections of the book provide an accessible introduction to quantum field theory and its relationship to classical systems, in addition to powerful perturbation techniques applicable to both classical and quantum problems. This book transforms abstract theoretical concepts into practical understanding through rigorous mathematical and numerical frameworks and illuminating examples, making it ideally suited for advanced undergraduate and postgraduate students enrolled on physics, applied mathematics, engineering and materials science courses.
Key Features:
Connects traditional mechanical concepts with modern physics.
Includes several worked examples, in addition to end-of-chapter problems and further reading to support teaching and learning.
Features seven appendices covering further topics such as mathematical preliminaries, numerical solutions to first-order and second-order differential equations and the Euler-Lagrange variational principle.
Contents
SECTION I General considerations
Chapter 1 Classification of Dynamics and Scope of This Book
SECTION II Linear dynamics of particles and objects
Chapter 2 Dynamics of Particles and Objects in Configuration Space
Chapter 3 Dynamics of Particles and Objects in Phase Space
SECTION III Linear dynamics of interacting particles
Chapter 4 Dynamics of Linear Molecules and Linear Atomic Chains
Chapter 5 Dynamics of Two- and Three-Dimensional Crystals
SECTION IV Nonlinear dynamics
Chapter 6 Non-linear Motion and Chaos - Theory
Chapter 7 Non-linear Motion and Chaos - Applications
SECTION V Elements of classical field theory
Chapter 8 Lagrangian and Hamiltonian of a Classical Field
SECTION VI Beyond classical mechanics
Chapter 9 Elements of Quantum Field Theory
Chapter 10 Classical and Quantum Perturbation Theories
Appendix A Mathematical Preliminaries
Appendix B Conservative Property of Central Forces
Appendix C Euler-Lagrange Variational Principle
Appendix D Introduction to Matrix Eigensolutions
Appendix E Reciprocal Lattice and Brillouin Zone
Appendix F Numerical Solution of Differential Equations
Appendix G Analytic Solution of Second Order Linear Inhomogeneous Differential
Equations
Answers to Selected Problems
References
Index
