# Physics 3320

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