### PREPARATORY READING

Note definitions, and bring any questions you have to class. These will be taken up each day.08/21/17: Introduction

0.0 Explanation of Course

08/23/17: 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

08/25/17: 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.

08/28/17: 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.

08/30/17: 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).

09/01/17: 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).

09/04/17: Labor Day, no class

09/06/17: 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

09/08/17: 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)

09/11/17: 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

09/13/17: 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

09/15/17: Chapter 4, continued; homework 4 assigned

4.7 Finite Rotations

4.8 Infinitesimal Rotations

09/18/17: Chapter 4, continued; homework 3 due

4.9 Rate of Change of a Vector

4.10 The Coriolis Effect

09/20/17: 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

09/22/17: 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

09/25/17: 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

09/27/17: Chapter 6

6.1 Formulation of the Problem

6.2 The Eigenvalue Equation and the Principal Axis Transformation

09/29/17: Chapter 6, continued; homework 6 assigned

6.3 Frequencies of Free Vibration, and Normal Coordinates

6.4 Free Vibrations of a Linear Triatomic Molecule

10/02/17: 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

10/04/17: Chapter 7

7.1 Basic Postulates of the Special Theory

7.2 Lorentz Transformations

7.3 Velocity Addition and Thomas Precession

10/06/17: Homecoming, no class

10/09/17: 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

10/10/17: Mid-term exam, 8:20pm-10:10pm, NPB 1002

10/11/17: 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

10/13/17: Chapter 7, continued; homework 8 assigned

7.10 Covariant Lagrangian Formulations

7.11 Introduction to the General Theory of Relativity

10/16/17: Chapter 8; homework 7 due

8.1 Legendre Transformations and the Hamilton Equations of Motion

8.2 Cyclic Coordinates and Conservation Theorems

10/18/17: Chapter 8, continued

8.3 Routh's Procedure

8.4 The Hamiltonian Formulation of Relativistic Mechanics

10/20/17: Chapter 8, continued; homework 9 assigned

8.5 Derivation of Hamilton's Equations from a Variational Principle

8.6 The Principle of Least Action

10/23/17: Chapter 9; homework 8 due

9.1 The Equations of Canonical Transformation

9.2 Examples of Canonical Transformations

9.3 The Harmonic Oscillator

10/25/17: 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

10/27/17: 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

10/30/17: 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

11/01/17: Chapter 10, continued

10.3 The Hamilton-Jacobi Equation for Hamilton's Characteristic Function

10.4 Separation of Variables in the Hamilton-Jacobi Equation

11/03/17: 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

11/06/17: Chapter 10, continued; homework 10 due

10.7 Action-Angle Variables for Completely Separable Systems

10.8 The Kepler Problem in Action-angle Variables

11/08/17: Chapter 11; Homework 12 assigned

11/10/17: Veterans Day, no class

11/13/17: Chapter 12; homework 11 due

12.1 Introduction

12.2 Time-dependent Perturbation Theory

11/15/17: Chapter 12, continued

12.3 Illustrations of Time-dependent Perturbation Theory

11/17/17: Chapter 12, continued; Homework 13 assigned

12.4 Time-independent Perturbation

11/20/17: Chapter 12, continued; homework 12 due

12.5 Adiabatic Invariants

11/22/17: Thanksgiving break, no class

11/24/17: Thanksgiving break, no class

11/27/17: Chapter 13; homework 13 due

13.1 The Transition from a Discrete to a Continuous System

13.2 The Lagrangian Formulation for Continuous Systems

11/29/17: Chapter 13, continued;

13.3 The Stress-energy Tensor and Conservation Theorems

12/01/17: Chapter 13, continued; homework 14 assigned

13.4 Hamiltonian Formulation

12/04/17: Chapter 13, continued

13.5 Relativistic Field Theory

13.6 Examples of Relativistic Field Theories

12/06/17: Chapter 13, continued

13.7 Noether's Theorem

12/08/17: Reading Day

12/11/17: Homework 14 due

12/13/17: Final exam, 3:00pm-5:00pm, NPB 1101