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283 pages

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English

This book is a one semester undergraduate textbook covering topics in classical mechanics at an intermediate level.

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Content

“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.- 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