Physics 306: Advanced Classical Mechanics

Course Description
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Syllabus

I. Newtonian Mechanics — Single Particle
         1.1 Newton's Laws
                  Newton's First Law, Second Law, and Third Law
                  principle of equivalence
         1.2 Conservation Theorems
                  impulse and linear momentum
                  torque and angular momentum
                  work and kinetic energy
                  conservative forces and potential energy
         1.3 The Equation of Motion for a Particle and Numerical Methods
                  retarding forces
                  motion of a body with variable mass
                  rocket motion

II. Gravitation
         2.1 Newton's Law of Universal Gravitation
         2.2 Gravitational Potential
         2.3 Ocean Tides

III. Central-Force Motion
         3.1 Velocity and Acceleration in Polar Coordinates
         3.2 Potential Energy and Angular Momentum in a Central Field
         3.3 Orbit of a Particle in a Central Field
         3.4 Kepler's Laws of Planetary Motion
         3.5 Motion in an Inverse-Square Repulsive Field
                  Rutherford scattering formula
                  cross sections

IV. Dynamics of a System of Particles
         4.1 Center of Mass
         4.2 Linear Momentum of the System
         4.3 Angular Momentum of the System
         4.4 Energy of the System

V. Motion in a Non inertial Reference Frame
         5.1 Rotating Coordinate Systems
         5.2 Centrifugal and Coriolis Forces
         5.3 Effects of the Earth's Rotation, the Foucault Pendulum

VI. Mechanics of Rigid Bodies
         6.1 Inertia Tensor
         6.2 A General Theorem Concerning Angular Momentum
         6.3 Laminar Motion of a Rigid Body
         6.4 Principal Axes of Inertia
         6.5 Euler's Equations for a Rigid Body

VII. Hamilton's Principle — Lagrangian and Hamiltonian Dynamics
         7.1 Hamilton's Principle
         7.2 Generalized Coordinates and Forces
         7.3 Lagrange's Equations of Motion in Generalized Coordinates
         7.4 Canonical Equations of Motion — Hamiltonian Dynamics

VIII. Chaos
         8.1 An Example — Driven Pendulum
                  phase space
                  Poincaré diagrams
                  bifurcation diagrams
         8.2 Toward an Understanding of Chaos
                  the route of period doubling to chaos
                  Feigenbaum number
                  Lyapunov exponents
         8.3 Fractals