33-332 Physical Mechanics II

Course Overview

Physical Mechanics II is the second course in a two-semester sequence on advanced classical mechanics for physics majors. The course will begin with a review of coordinate systems, frames of reference, Newton's laws, and the concepts of energy, momentum, and angular momentum. Motion in noninertial reference frames and perturbation theory will then be studied, followed by the dynamics of rigid bodies, coupled oscillations, and nonlinear oscillations and chaos. Time permitting, Hamiltonian dynamics will be introduced. As in the first semester, this course is a quantitative one and will require the use of advanced mathematics to solve more difficult physical problems.

Course Outline

• Review (Chapters 1 and 2)
  • frames of reference and coordinate systems
  • vectors and vector calculus
  • velocity and acceleration
  • Newton's laws
  • energy, momentum, angular momentum, force, torque
  • Lagrangian methods, principle of least action
  • friction, drag, gravitation
• Motion in a noninertial reference frame (Chapter 10)
  • rotating and accelerating frames of reference
  • centrifugal and coriolis forces
  • motion relative to the earth
  • perturbation theory
• Dynamics of rigid bodies (Chapter 11)
  • inertia tensor
  • angular momentum
  • principal axes of inertia
  • moments of inertia
  • rotations and Eulerian angles
  • Euler's equations for a rigid body
  • the symmetric top (force-free and subject to gravity)
  • stability of rigid body rotations
• Coupled small oscillations (Chapter 12)
  • general problem of coupled small oscillations
  • characteristic frequencies and normal modes
• Nonlinear oscillations and chaos (Chapter 4)
  • butterfly effect and sensitivity to initial conditions
  • phase space and trajectories
  • dissipative systems and attractors
  • Poincare surfaces of section
  • logistic map and period doubling route to chaos
  • identification of chaos, Lyapunov exponents
  • fractals
  • damped, sinusoidally-driven pendulum
  • forced and damped inverted pendulum (Duffing oscillator)
• Hamiltonian dynamics (Chapter 7)
  • Hamilton's equations
  • Poisson brackets
  • canonical transformations

Test Dates

Final Examination