**Advanced Topics**

Physics 4322 Syllabus

Physics 4322 Syllabus

**Part I: Modern Introductory Mechanics**

**Chapter 8: The Two Body Central Force Problem**

Relative coordinates

Runge-Lenz treatment of Coulomb force

Lagrangian equations of motion

Celestial mechanics

General Relativity modification

Orbital stability

Virial theorem

**Chapter 9: Scattering and Collisions of Particles**

Multi-particle conservation laws

Coulomb scattering

Differential cross sections

Rutherford scattering in the center of mass frame

Simple treatment of light deflection

Cross section cookbook

Connection between Lab and CM frames

A kinematical example in the Lab frame

Rutherford scattering in the laboratory frame

Total cross section

**Chapter 10: Non inertial Reference Frames**

Finite displacements and rotations

Instantaneous relations for velocity, acceleration

Useful Earth coordinate choices

Deflection of projectiles near Earth¹s surface

Deflections for dropped objects

Focault pendulum

**Chapter 11: Rigid Body Motion**

Concept of a rigid body

Instantaneous kinetic energy in body frame

Angular momentum and the inertia tensor

Transformation properties of the inertia tensor

Principal axes

Parallel axis theorem

Euler angles

Euler¹s equations of motion

Symmetrical top Euler solution

Symmetrical top Lagrangian solution

**Chapter 12: Coupled Oscillations**

Coupled dynamical equations

Eigenvalue/eigenvector solution

Examples

Weak/strong coupling

Example using mechanical/electrical analogy

**Chapter 13: Special Relativity**

Invariance and covariance

Two postulates of special relativity

Lorentz tranformations deduced

Alternate notation for Lorentz transformations

The ³light cone² and tachyons

Mathematical properties of Lorentz transformations

Consequences of relativity

Velocity addition law

Momentum and energy united

Four short points

**Part II: Electrodynamics**

**Chapter 1: Electromagnetic Waves**

The Wave Equation in One Dimension

One Dimensional Scattering

Two Dimensional Scattering

Electromagnetic Plane Waves

Electromagnetic Scattering – Nonconducting Case

Electromagnetic Scattering – Conducting Case

Model of Constuitive Relations for Nonconductors

Wave Guides

**Chapter 2: Potentials and Fields**

Potential formulation

Gauge transformations

Retarded potentials

Point particle fields

Moving point particle field example

**Chapter 3: Radiation**

Arbitrary source radiation

Multipole expansion

Electric and magnetic multipole results

Lienard result and circular accelerators