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Search and navigate content across your entire Bookshelf library. Interactive notebook and read-aloud functionality. Look up additional information online by highlighting a word or phrase. 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. Table of Contents. PrefaceChapter 1.
Matrices and Vectors1.1 Introduction1.2 The Concept of a Scalar1.3 Coordinate Transformations1.4 Properties of Rotation Matrices1.5 Matrix Operations1.6 Further Definitions1.7 Geometrical Significance of Transformation Matrices1.8 Definitions of a Scalar and a Vector in Terms of Transformation Properties1.9 Elementary Scalar and Vector Operations1.10 The Scalar Product of Two Vectors1.11 The Vector Product of Two Vectors1.12 Unit VectorsSuggested ReferencesProblemsChapter 2. Vector Calculus2.1 Introduction2.2 Differentiation of a Vector with Respect to a Scalar2.3 Examples of Derivatives —Velocity and Acceleration2.4 Angular Velocity2.5 The Gradient Operator2.6 The Divergence of a Vector2.7 The Curl of a Vector2.8 Some Additional Differential Vector Relations2.9 Integration of VectorsSuggested ReferencesProblemsChapter 3. Fundamentals of Newtonian Mechanics3.1 Introduction3.2 Newton's Laws3.3 Frames of Reference3.4 The Equation of Motion for a Particle3.5 Conservation Theorems3.6 Conservation Theorems for a System of Particles3.7 Limitations of Newtonian MechanicsSuggested ReferencesProblemsChapter 4. The Special Theory of Relativity4.1 Introduction4.2 Galilean Invariance4.3 The Lorentz Transformation4.4 Momentum and Energy in Relativity4.5 Some Consequences of the Lorentz TransformationSuggested ReferencesProblemsChapter 5. Gravitational Attraction and Potentials5.1 Introduction5.2 The Gravitational Potential5.3 Lines of Force and Equipotential Surfaces5.4 The Gravitational Potential of a Spherical Shell5.5 A Final CommentSuggested ReferencesProblemsChapter 6. Oscillatory Motion6.1 Introduction6.2 The Simple Harmonic Oscillator6.3 Damped Harmonic Motion6.4 Forcing Functions6.5 Forced Oscillations6.6 Phase Diagrams6.7 The Response of Linear Oscillators to Impulsive Forcing Functions6.8 Electrical Oscillations6.9 Harmonic Oscillations in Two Dimensions6.10 The Use of Complex NotationSuggested ReferencesProblems 7Chapter 7. Nonlinear Oscillations7.1 Oscillations7.2 Oscillations for General Potential Functions7.3 Phase Diagrams for Nonlinear Systems7.4 The Plane Pendulum7.5 Nonlinear Oscillations in a Symmetric Potential - The Method of Successive Approximations7.6 Nonlinear Oscillations in an Asymmetric Potential - The Method of PerturbationsSuggested ReferencesProblemsChapter 8.
Some Methods in the Calculus of Variations8.1 Introduction8.2 Statement of the Problem8.3 Euler's Equation8.4 The Brachistochrone Problem8.5 The 'Second Form' of Euler's Equation8.6 Functions with Several Dependent Variables8.7 The Euler Equations When Auxiliary Conditions Are Imposed8.8 The δ NotationSuggested ReferencesProblemsChapter 9.