Note definitions, and bring any questions you have to class. These will be taken up each day.

08/22/16: Introduction
0.0 Explanation of Course
08/24/16: Chapter 1
Coordinate transformations, vectors and co-vectors, the metric
1.1 Mechanics of a Particle
1.2 Mechanics of a System of Particles
1.3 Constraints
08/26/16: Homework 1 assigned
Read section i) on constraints, the Intro to Relativity, and
describe the motion a pendulum fully in cartesian coordinates
1.4 D'Alembert's Principle and Lagrange's Equations
1.5 Velocity-Dependent Potentials and the Dissipation Function
1.6 Simple Applications of the Lagrangian Formulation
Suggestion: Consider doing problems 1.8, 1.9 (spot the error) and 1.10 as exercises.

08/29/16: Chapter 2
2.1 Hamilton's Principle
2.2 Some Techniques of the Calculus of Variations
2.3 Derivation of Lagrange's Equations from Hamilton's Principle
Suggestion: Examine how the kinetic energy of a particle changes under a coordinate transformation.
08/31/16: Chapter 2, continued
2.4 Extension of Hamilton's Principle to Non-holonomic Systems
2.5 Advantages of a Variational Principle Formulation
2.6 Conservation Theorems and Symmetry Properties
2.7 Energy Function and the Conservation of Energy
Suggestion: Write out the analysis of sliding off a sphere.
(Caution, both the book and the official list of errors have errors in them on this problem).
09/02/16: Chapter 3; homework 2 assigned; homework 1 due
3.1 Reduction to the Equivalent One-Body Problem
3.2 The Equations of Motion and First Integrals
3.3 The Equivalent One-Dimensional Problem, and Classification of Orbits
3.4 The Virial Theorem

Suggestion: Remember to count (degrees of freedom).
09/05/16: Labor Day, no class
09/07/16: Chapter 3, continued
3.5 The Differential Equation for the Orbit, and Integrable Power-Law Potentials
3.6 (Conditions for Closed Orbits: Bertrand's Theorem)
3.7 The Kepler Problem: Inverse-Square Law of Force
3.8 The Motion in Time in the Kepler Problem
09/09/16: Chapter 3 continued; homework 3 assigned
3.9 The Laplace-Runge-Lenz Vector
3.10 Scattering in a Central Force Field
3.11 Transformation of the Scattering Problem to Laboratory Coordinates
3.12 (The Three-Body Problem)

09/12/16: Chapter 4, homework 2 due
4.1 The Independent Coordinates of a Rigid Body
4.2 Orthogonal Transformations
4.3 Formal Properties of the Transformation Matrix
09/14/16: Chapter 4, continued
4.4 The Euler Angles
4.5 The Cayley-Klein Parameters and Related Quantities
4.6 Euler's Theorem on the Motion of a Rigid Body
09/16/16: Chapter 4, continued; homework 4 assigned
4.7 Finite Rotations
4.8 Infinitesimal Rotations

09/19/16: Chapter 4, continued; homework 3 due
4.9 Rate of Change of a Vector
4.10 The Coriolis Effect
09/21/16: Chapter 5
5.1 Angular Momentum and Kinetic Energy of Motion about a Point
5.2 Tensors
5.3 The Inertia Tensor and the Moment of Inertia
09/23/16: Chapter 5, continued; homework 5 assigned
5.4 The Eigenvalues of the Inertia Tensor and the Principal Axis Transformation
5.5 Solving Rigid Body Problems and the Euler Equations of Motion
5.6 Torque-free Motion of a Rigid Body

09/26/16: Chapter 5, continued; homework 4 due
5.7 The Heavy Symmetrical Top with One Point Fixed
5.8 Precession of the Equinoxes and of Satellite Orbits
5.9 Precession of Systems of Charges in a Magnetic Field
09/28/16: Chapter 6
6.1 Formulation of the Problem
6.2 The Eigenvalue Equation and the Principal Axis Transformation
09/30/16: Chapter 6, continued; homework 6 assigned
6.3 Frequencies of Free Vibration, and Normal Coordinates
6.4 Free Vibrations of a Linear Triatomic Molecule

10/03/16: Chapter 6, continued; homework 5 due
6.5 Forced Vibrations and the Effect of Dissipative Forces
6.6 Beyond Small Oscillations; The Damped Driven Pendulum and the Josephson Junction
10/05/16: Chapter 7
7.1 Basic Postulates of the Special Theory
7.2 Lorentz Transformations
7.3 Velocity Addition and Thomas Precession
10/07/16: Chapter 7, continued; homework 7 assigned
7.4 Vectors and the Metric Tensor
7.5 1-Forms and Tensors
7.6 Forces in the Special Theory; Electromagnetism

10/10/16: Chapter 7, continued; homework 6 due
7.7 Relativistic Kinematics of Collisions and Many-Particle Systems
7.8 Relativistic Angular Momentum
7.9 The Lagrangian Formulation of Relativistic Mechanics
10/12/16: Chapter 7, continued; homework 8 assigned
7.10 Covariant Lagrangian Formulations
7.11 Introduction to the General Theory of Relativity
10/14/16: Homecoming, no class

10/17/16: Chapter 8; homework 7 due
8.1 Legendre Transformations and the Hamilton Equations of Motion
8.2 Cyclic Coordinates and Conservation Theorems
10/19/16: Chapter 8, continued
8.3 Routh's Procedure
8.4 The Hamiltonian Formulation of Relativistic Mechanics
10/21/16: Chapter 8, continued; homework 9 assigned
8.5 Derivation of Hamilton's Equations from a Variational Principle
8.6 The Principle of Least Action

10/24/16: Chapter 9; homework 8 due
9.1 The Equations of Canonical Transformation
9.2 Examples of Canonical Transformations
9.3 The Harmonic Oscillator
10/26/16: Chapter 9, continued
9.4 The Symplectic Approach to Canonical Transformations
9.5 Poisson Brackets and Other Canonical Invariants
9.6 Equations of Motion, Infinitesimal Canonical Transformations, and Conservation Theorems in the Poisson Bracket Formulation
10/28/16: Chapter 9, continued; homework 10 assigned
9.7 The Angular Momentum Poisson Bracket Relations
9.8 Symmetry Groups of Mechanical Systems
9.9 Liouville's Theorem

10/31/16: Chapter 10; homework 9 due
10.1 The Hamilton-Jacobi Equation for Hamilton's Principal Function
10.2 The Harmonic Oscillator Problem as an Example of the Hamilton-Jacobi Method
11/02/16: Chapter 10, continued
10.3 The Hamilton-Jacobi Equation for Hamilton's Characteristic Function
10.4 Separation of Variables in the Hamilton-Jacobi Equation
11/04/16: Chapter 10, continued; homework 11 assigned
10.5 Ignorable Coordinates and the Kepler Problem
10.6 Action-angle Variables in Systems of One Degree of Freedom

11/07/16: Chapter 10, continued; homework 10 due
10.7 Action-Angle Variables for Completely Separable Systems
10.8 The Kepler Problem in Action-angle Variables
11/09/16: Chapter 11; Homework 12 assigned
11/11/16: Veterans Day, no class

11/14/16: Chapter 12; homework 11 due
12.1 Introduction
12.2 Time-dependent Perturbation Theory
11/16/16: Chapter 12, continued
12.3 Illustrations of Time-dependent Perturbation Theory
11/18/16: Chapter 12, continued; Homework 13 assigned
12.4 Time-independent Perturbation

11/21/16: Chapter 12, continued; homework 12 due
11/23/16: Thanksgiving break, no class
11/25/16: Thanksgiving break, no class

11/28/16: Chapter 13; homework 13 due
13.1 The Transition from a Discrete to a Continuous System
13.2 The Lagrangian Formulation for Continuous Systems
11/30/16: Chapter 13, continued;
13.3 The Stress-energy Tensor and Conservation Theorems
12/02/16: Chapter 13, continued; homework 14 assigned
13.4 Hamiltonian Formulation

12/05/16: Chapter 13, continued
13.5 Relativistic Field Theory
13.6 Examples of Relativistic Field Theories
12/07/16: Chapter 13, continued
13.7 Noether's Theorem