w-efab571e92.pdf

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
Euler-Lagrange 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 (1983-1985), 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 Member-at-Large for the Texas Section of the American Physical Society (TSAPS) for 2013-2016.

Dr. Wilcox's publications on INSPIRE