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