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Classical Dynamics of Particles and Systems

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ISBN-10: 0534408966

ISBN-13: 9780534408961

Edition: 5th 2004 (Revised)

Authors: Stephen T. Thornton, Jerry B. Marion

List price: $375.95
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This best-selling classical mechanics text, written for the advanced undergraduate one- or two-semester course, provides a complete account of the classical mechanics of particles, systems of particles, and rigid bodies. Vector calculus is used extensively to explore topics.The Lagrangian formulation of mechanics is introduced early to show its powerful problem solving ability.. Modern notation and terminology are used throughout in support of the text's objective: to facilitate students' transition to advanced physics and the mathematical formalism needed for the quantum theory of physics. CLASSICAL DYNAMICS OF PARTICLES AND SYSTEMS can easily be used for a one- or two-semester course,…    
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Book details

List price: $375.95
Edition: 5th
Copyright year: 2004
Publisher: Brooks/Cole
Publication date: 7/7/2003
Binding: Hardcover
Pages: 672
Size: 7.50" wide x 9.25" long x 1.25" tall
Weight: 2.882
Language: English

Matrices, Vectors, and Vector Calculus
Concept of a Scalar
Coordinate Transformations
Properties of Rotation Matrices
Matrix Operations
Further Definitions
Geometrical Significance of Transformation Matrices
Definitions of a Scalar and a Vector in Terms of Transformation Properties
Elementary Scalar and Vector Operations
Scalar Product of Two Vectors
Unit Vectors
Vector Product of Two Vectors
Differentiation of a Vector with Respect to a Scalar
Examples of Derivatives--Velocity and Acceleration
Angular Velocity
Gradient Operator
Integration of Vectors
Newtonian Mechanics--Single Particle
Newton's Laws
Frames of Reference
The Equation of Motion for a Particle
Conservation Theorems
Limitations of Newtonian Mechanics
Simple Harmonic Oscillator
Harmonic Oscillations in Two Dimensions
Phase Diagrams
Damped Oscillations
Sinusoidal Driving Forces
Physical Systems
Principle of Superposition--Fourier Series
The Response of Linear Oscillators to Impulsive Forcing Functions (Optional)
Nonlinear Oscillations and Chaos
Nonlinear Oscillations
Phase Diagrams for Nonlinear Systems
Plane Pendulum
Jumps, Hysteresis, and Phase Lags
Chaos in a Pendulum
Chaos Identification
Gravitational Potential
Lines of Force and Equipotential Surfaces
When Is the Potential Concept Useful?
Ocean Tides
Some Methods in the Calculus of Variations
Statement of the Problem
Euler's Equation
The "Second Form" of the Euler Equation
Functions with Several Dependent Variables
Euler Equations When Auxiliary Conditions Are Imposed
The [delta] Notation
Hamilton's Principle--Lagrangian and Hamiltonian Dynamics
Hamilton's Principle
Generalized Coordinates
Lagrange's Equations of Motion in Generalized Coordinates
Lagrange's Equations with Undetermined Multipliers
Equivalence of Lagrange's and Newton's Equations
Essence of Lagrangian Dynamics
A Theorem Concerning the Kinetic Energy
Conservation Theorems Revisited
Canonical Equations of Motion--Hamiltonian Dynamics
Some Comments Regarding Dynamical Variables and Variational Calculations in Physics
Phase Space and Liouville's Theorem (Optional)
Virial Theorem (Optional)
Central-Force Motion
Reduced Mass
Conservation Theorems--First Integrals of the Motion
Equations of Motion
Orbits in a Central Field
Centrifugal Energy and the Effective Potential
Planetary Motion--Kepler's Problem
Orbital Dynamics
Apsidal Angles and Precession (Optional)
Stability of Circular Orbits (Optional)
Dynamics of a System of Particles
Center of Mass
Linear Momentum of the System
Angular Momentum of the System
Energy of the System
Elastic Collisions of Two Particles
Kinematics of Elastic Collisions
Inelastic Collisions
Scattering Cross Sections
Rutherford Scattering Formula
Rocket Motion
Motion in a Nonintertial Reference Frame
Rotating Coordinate Systems
Centrifugal and Coriolis Forces
Motion Relative to the Earth
Dynamics of Rigid Bodies
Simple Planar Motion
Inertia Tensor
Angular Momentum
Principal Axes of Inertia
Moments of Inertia for Different Body Coordinate Systems
Further Properties of the Inertia Tensor
Eulerian Angles
Euler's Equations for a Rigid Body
Force-Free Motion of a Symmetric Top
Motion of a Symmetric Top with One Point Fixed
Stability of Rigid-Body Rotations
Coupled Oscillations
Two Coupled Harmonic Oscillators
Weak Coupling
General Problem of Coupled Oscillations
Orthogonality of the Eigenvectors (Optional)
Normal Coordinates
Molecular Vibrations
Three Linearly Coupled Plane Pendula--an Example of Degeneracy
The Loaded String
Continuous Systems; Waves
Continuous String as a Limiting Case of the Loaded String
Energy of a Vibrating String
Wave Equation
Forced and Damped Motion
General Solutions of the Wave Equation
Separation of the Wave Equation
Phase Velocity, Dispersion, and Attenuation
Group Velocity and Wave Packets
Special Theory of Relativity
Galilean Invariance
Lorentz Transformation
Experimental Verification of the Special Theory
Relativistic Doppler Effect
Twin Paradox
Relativistic Momentum
Spacetime and Four-Vectors
Lagrangian Function in Special Relativity
Relativistic Kinematics
Taylor's Theorem
Elliptic Integrals
Elliptic Integrals of the First Kind
Elliptic Integrals of the Second Kind
Elliptic Integrals of the Third Kind
Ordinary Differential Equations of Second Order
Linear Homogeneous Equations
Linear Inhomogeneous Equations
Useful Formulas
Binomial Expansion
Trigonometric Relations
Trigonometric Series
Exponential and Logarithmic Series
Complex Quantities
Hyperbolic Functions
Useful Integrals
Algebraic Functions
Trigonometric Functions
Gamma Functions
Differential Relations in Different Coordinate Systems
Rectangular Coordinates
Cylindrical Coordinates
Spherical Coordinates
A "Proof" of the Relation [characters not reproducible] = [characters not reproducible]
Numerical Solution for Example 2.7
Selected References
Answers to Even-Numbered Problems