### COURSE SCHEDULE

08/22/18: Begin 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

08/24/18: Finish Chapter 1

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

08/27/18: Begin 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

08/29/18: Finish Chapter 2

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

08/31/18: Begin Chapter 3

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

09/03/18: Labor Day, no class

09/05/18: Continue with Chapter 3

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

09/07/18: Finish Chapter 3

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)

09/10/18: Begin Chapter 4

4.1 The Independent Coordinates of a Rigid Body

4.2 Orthogonal Transformations

4.3 Formal Properties of the Transformation Matrix

09/12/18: Continue with Chapter 4

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

09/14/18: Continue with Chapter 4

4.7 Finite Rotations

4.8 Infinitesimal Rotations

09/17/18: Finish Chapter 4

4.9 Rate of Change of a Vector

4.10 The Coriolis Effect

09/19/18: Begin 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

09/21/18: Continue with Chapter 5

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

09/24/18: Finish Chapter 5

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

09/26/18: Begin Chapter 6

6.1 Formulation of the Problem

6.2 The Eigenvalue Equation and the Principal Axis Transformation

09/28/18: Continue with Chapter 6

6.3 Frequencies of Free Vibration, and Normal Coordinates

6.4 Free Vibrations of a Linear Triatomic Molecule

10/01/18: Finish Chapter 6

6.5 Forced Vibrations and the Effect of Dissipative Forces

6.6 Beyond Small Oscillations; The Damped Driven Pendulum and the Josephson Junction

### 10/03/18: EXAM 1 (Periods E2-E3) on Chapters 1-6

10/05/18: Begin Chapter 77.1 Basic Postulates of the Special Theory

7.2 Lorentz Transformations

7.3 Velocity Addition and Thomas Precession

10/08/18: Continue with Chapter 7

7.4 Vectors and the Metric Tensor

7.5 1-Forms and Tensors

7.6 Forces in the Special Theory; Electromagnetism

10/10/18: Continue Chapter 7

7.7 Relativistic Kinematics of Collisions and Many-Particle Systems

7.8 Relativistic Angular Momentum

7.9 The Lagrangian Formulation of Relativistic Mechanics

10/12/18: Finish Chapter 7

7.10 Covariant Lagrangian Formulations

7.11 Introduction to the General Theory of Relativity

10/15/18: Begin Chapter 8

8.1 Legendre Transformations and the Hamilton Equations of Motion

8.2 Cyclic Coordinates and Conservation Theorems

10/17/18: Continue with Chapter 8

8.3 Routh's Procedure

8.4 The Hamiltonian Formulation of Relativistic Mechanics

10/19/18: Finish Chapter 8

8.5 Derivation of Hamilton's Equations from a Variational Principle

8.6 The Principle of Least Action

10/22/18: Begin Chapter 9

9.1 The Equations of Canonical Transformation

9.2 Examples of Canonical Transformations

9.3 The Harmonic Oscillator

10/24/18: Continue with Chapter 9

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

10/26/18: Finish Chapter 9

9.7 The Angular Momentum Poisson Bracket Relations

9.8 Symmetry Groups of Mechanical Systems

9.9 Liouville's Theorem

10/29/18: Begin Chapter 10

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

10/31/18: Continue with Chapter 10

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

10.4 Separation of Variables in the Hamilton-Jacobi Equation

11/02/18: UF Homecoming, no class

11/05/18: Continue with Chapter 10

10.5 Ignorable Coordinates and the Kepler Problem

10.6 Action-angle Variables in Systems of One Degree of Freedom

11/07/18: Finish Chapter 10

10.7 Action-Angle Variables for Completely Separable Systems

10.8 The Kepler Problem in Action-angle Variables

11/09/18: Chapter 11

11/12/18: Veterans Day Holiday, no class

11/14/18: Begin Chapter 12

12.1 Introduction

12.2 Time-dependent Perturbation Theory

11/16/18: Continue with Chapter 12

12.3 Illustrations of Time-dependent Perturbation Theory

12.4 Time-independent Perturbation

11/19/18: Finish Chapter 12

12.5 Adiabatic Invariants

11/21/18: Thanksgiving break, no class

11/23/18: Thanksgiving break, no class

11/26/18: Begin Chapter 13

13.1 The Transition from a Discrete to a Continuous System

13.2 The Lagrangian Formulation for Continuous Systems

11/28/18: Continue with Chapter 13

13.3 The Stress-energy Tensor and Conservation Theorems

13.4 Hamiltonian Formulation

11/30/18: Continue with Chapter 13

13.5 Relativistic Field Theory

13.6 Examples of Relativistic Field Theories

12/03/18: Finish Chapter 13

13.7 Noether's Theorem