Classical Dynamics of Particles and Systems
Published on 22. October 2013
592 pages
978-1-4832-7281-8 (ISBN)
Description
Classical Dynamics of Particles and Systems presents a modern and reasonably complete account of the classical mechanics of particles, systems of particles, and rigid bodies for physics students at the advanced undergraduate level. The book aims to present a modern treatment of classical mechanical systems in such a way that the transition to the quantum theory of physics can be made with the least possible difficulty; to acquaint the student with new mathematical techniques and provide sufficient practice in solving problems; and to impart to the student some degree of sophistication in handling both the formalism of the theory and the operational technique of problem solving. Vector methods are developed in the first two chapters and are used throughout the book. Other chapters cover the fundamentals of Newtonian mechanics, the special theory of relativity, gravitational attraction and potentials, oscillatory motion, Lagrangian and Hamiltonian dynamics, central-force motion, two-particle collisions, and the wave equation.
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Content
PrefaceChapter 1. Matrices and Vectors 1.1 Introduction 1.2 The Concept of a Scalar 1.3 Coordinate Transformations 1.4 Properties of Rotation Matrices 1.5 Matrix Operations 1.6 Further Definitions 1.7 Geometrical Significance of Transformation Matrices 1.8 Definitions of a Scalar and a Vector in Terms of Transformation Properties 1.9 Elementary Scalar and Vector Operations 1.10 The Scalar Product of Two Vectors 1.11 The Vector Product of Two Vectors 1.12 Unit Vectors Suggested References ProblemsChapter 2. Vector Calculus 2.1 Introduction 2.2 Differentiation of a Vector with Respect to a Scalar 2.3 Examples of Derivatives -Velocity and Acceleration 2.4 Angular Velocity 2.5 The Gradient Operator 2.6 The Divergence of a Vector 2.7 The Curl of a Vector 2.8 Some Additional Differential Vector Relations 2.9 Integration of Vectors Suggested References ProblemsChapter 3. Fundamentals of Newtonian Mechanics 3.1 Introduction 3.2 Newton's Laws 3.3 Frames of Reference 3.4 The Equation of Motion for a Particle 3.5 Conservation Theorems 3.6 Conservation Theorems for a System of Particles 3.7 Limitations of Newtonian Mechanics Suggested References ProblemsChapter 4. The Special Theory of Relativity 4.1 Introduction 4.2 Galilean Invariance 4.3 The Lorentz Transformation 4.4 Momentum and Energy in Relativity 4.5 Some Consequences of the Lorentz Transformation Suggested References Problems Chapter 5. Gravitational Attraction and Potentials 5.1 Introduction 5.2 The Gravitational Potential 5.3 Lines of Force and Equipotential Surfaces 5.4 The Gravitational Potential of a Spherical Shell 5.5 A Final Comment Suggested References ProblemsChapter 6. Oscillatory Motion 6.1 Introduction 6.2 The Simple Harmonic Oscillator 6.3 Damped Harmonic Motion 6.4 Forcing Functions 6.5 Forced Oscillations 6.6 Phase Diagrams 6.7 The Response of Linear Oscillators to Impulsive Forcing Functions 6.8 Electrical Oscillations 6.9 Harmonic Oscillations in Two Dimensions 6.10 The Use of Complex Notation Suggested References Problems 7Chapter 7. Nonlinear Oscillations 7.1 Oscillations 7.2 Oscillations for General Potential Functions 7.3 Phase Diagrams for Nonlinear Systems 7.4 The Plane Pendulum 7.5 Nonlinear Oscillations in a Symmetric Potential - The Method of Successive Approximations 7.6 Nonlinear Oscillations in an Asymmetric Potential - The Method of Perturbations Suggested References ProblemsChapter 8. Some Methods in the Calculus of Variations 8.1 Introduction 8.2 Statement of the Problem 8.3 Euler's Equation 8.4 The Brachistochrone Problem 8.5 The "Second Form" of Euler's Equation 8.6 Functions with Several Dependent Variables 8.7 The Euler Equations When Auxiliary Conditions Are Imposed 8.8 The d Notation Suggested References ProblemsChapter 9. Hamilton's Principle - Lagrangian and Hamiltonian Dynamics 9.1 Introduction 9.2 Hamilton's Principle 9.3 Generalized Coordinates 9.4 Lagrange's Equations of Motion in Generalized Coordinates 9.5 Lagrange's Equations with Undetermined Multipliers 9.6 The Equivalence of Lagrange's and Newton's Equations 9.7 The Essence of Lagrangian Dynamics 9.8 A Theorem Concerning the Kinetic Energy 9.9 The Conservation of Energy 9.10 The Conservation of Linear Momentum 9.11 The Conservation of Angular Momentum 9.12 The Canonical Equations of Motion - Hamiltonian Dynamics 9.13 Some Comments Regarding Dynamical Variables and Variational Calculations in Physics 9.14 Phase Space and Liouville's Theorem 9.15 The Virial Theorem 9.16 The Lagrangian Function in Special Relativity Suggested References ProblemsChapter 10. Central-Force Motion 10.
