Modern Introductory Mechanics

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
     Chapter 1 Problems

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 Stabilty in One Dimension
          Equilibrium and Stability in D Dimensions
     Chapter 2 Problems

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
     Chapter 3 Problems

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
     Chapter 4 Problems

5 Gravitation
     Newton’s Law of Gravitation
          Gravitational Potential
          Modifications for Extended Objects
          Eötvös Experiment on Composition Dependence of Gravitational Forces
     Chapter 5 Problems

6 Calculus of Variations
     Euler-Lagrange Equation
          Integrated 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
     Chapter 6 Problems

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 .
          Investigation into the Meaning of . (Optional)
          Hamilton’s Equations
          Holonomic Constraints in Hamiltonian Formalism
     Chapter 7 Problems

Endnotes