Modern Introductory Mechanics
Physics 3320 Syllabus
Chapter 1: Mathematical Review
- Trigonometry
- Matrices
- Orthogonal Transformations
- Scalars and Vector Fields
- Vector Algebra and Scalar Differentiation
- Alternate Coordinate Systems
- Angular Velocity
- Differential Operator and the 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 for Nonlinear Oscillations
- The Logistic Difference Equation
- Fractals
- Chaos in Physical Systems
- Dissipative Phase Space
- Lyapunov Exponents
- The Intermittant 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 ERquation
- “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
- Isoperimetic 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 dE/dt=0
- Hamilton’s Equations
- Holonomic Constraints in Hamiltonian Formalism
- Problems