Modern Introductory Mechanics
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About the book
Description
“Modern Introductory Mechanics, Part I” is a one semester undergraduate textbook covering topics in classical mechanics at an intermediate level. The coverage is rigorous but concise and accessible, with an emphasis on concepts and mathematical techniques which are basic to most fields of physics. Some advanced topics such as chaos theory, Green functions, variational methods and scaling techniques are included. The book concludes with a presentation of Lagrangian and Hamiltonian mechanics and associated conservation laws. Many homework problems directly associated with the text are included.
Cover artwork by Gerald Plant.Content
 Chapter 1: Mathematical Review
 Trigonometry
 Matrices
 Orthogonal Transformations
 Scalar and Vector Fields
 Vector Algebra and Scalar Differentiation
 Alternate Coordinate Systems
 Angular Velocity
 Differential Operators and Leibnitz Rule
 Complex Variables
 Problems
 Chapter 2: Newtonian Mechanics
 Review of Newton’s Laws
 Simple Examples using Newton’s Laws
 Single Particle Conservation Theorems
 Potential Energy and Particle Motion
 Equilibrium and Stability in One Dimension
 Equilibrium and Stability in D Dimensions
 Problems
 Chapter 3: Linear Oscillations
 General Restoring Forces in One and Two Dimensions
 Damped Oscillations
 Circuit/Oscillator Analogy
 Driven Harmonic Oscillations
 Fourier Series Methods
 Green Function Methods
 Problems
 Chapter 4: Nonlinear Oscillations
 The Anharmonic Oscillator
 The Plane Pendulum
 Phase Diagrams and Nonlinear Oscillations
 The Logistic Difference Equation
 Fractals
 Chaos in Physical Systems
 Dissipative Phase Space
 Lyapunov Exponents
 The Intermittent Transition to Chaos
 Problems
 Chapter 5: Gravitation
 Newton’s Law of Gravitation
 Gravitational Potential
 Modifications for Extended Objects
 Eötvös Experiment on Composition Dependence of...
 Gravitational Forces
 Problems
 Chapter 6: Calculus of Variations
 EulerLagrange Equation
 “Second form” of Euler’s Equation
 Brachistochrone Problem
 The Case of More than One Dependent Variable
 The Case of More than One Independent Variable
 Constraints
 Lagrange Multipliers
 Isoperimetric Problems
 Variation of the End Points of Integration
 Problems
 Chapter 7: Lagrangian and Hamiltonian Mechanics
 The Action and Hamilton's Principle
 Generalized Coordinates
 Examples of the Formalism
 Two Points about Lagrangian Methods
 Types of Constraints
 Endpoint Invariance: Multiparticle Conservation Laws
 Consequences of Scale Invariance
 When Does H=T+U?
 Investigation into the Meaning of...
 Hamilton’s Equations
 Holonomic Constraints in Hamiltonian Formalism
 Problems
About the Author
Walter Wilcox is Professor of physics and former graduate program director for the Baylor University Physics Department. He earned a PhD in elementary particle physics from UCLA in 1981 under the guidance of Dr. Julian Schwinger. He has also taught and done research at Oklahoma State University (1981–1983), TRIUMF Laboratory (19831985), and the University of Kentucky (1985–1986). He has been awarded grants from the National Science Foundation (NSF) in theoretical physics and, in collaboration with Dr. Ron Morgan, in applied mathematics. His research focuses on the development and use of numerical methods in the field of theoretical physics known as "lattice QCD". He is equally interested in teaching physics and has a number of textbooks published or in preparation, and is also presently serving as a MemberatLarge for the Texas Section of the American Physical Society (TSAPS) for 20132016.