Physics 301: Intermediate Mechanics

Course outline

Cartesian coordinates: vectors, index notation, rotation matrices

Newton’s Laws: integrable cases, drag forces, ballistics, rocket motion

Work and Energy: kinetic energy, conservative forces, phase space

Oscillations: driven and damped, resonance, Fourier series, impulse response, Green’s functions

Polar coordinates: cylindrical and spherical polars, unit vectors, Del operator, velocity and acceleration in polars

Gravitation: field and potential, spherical shell

Calculus of variations: Euler equation, brachistochrone, Lagrange multipliers

Lagrangian mechanics: generalized coordinates, Euler-Lagrange equations, constraints, conservation laws

Hamiltonian mechanics: canonical equations, cyclic coordinates, Hamiltonian phase space, Liouville’s theorem, virial theorem

Central force motion: equivalent one-body problem, reduced mass, effective potential, Kepler orbits, scattering

Non-inertial frames: centrifugal and Coriolis forces

Systems of particles: centre of mass, general theorems, rigid bodies, inertia tensor

Coupled oscillations: general formalism, eigenfrequencies, normal modes, loaded string

Continuous media: strings, wave equation, dispersion and attenuation

Organization

Lectures Tu, Th 9:25-10:40 AM,

Problem session Tu 2:30 - 3:50 PM

Homework (35%) Problems assigned weekly

Term exam (30%)

Final exam (35%)

Text: Marion and Thornton, Classical Dynamics of Particles and Systems

Lecture notes and problem solutions available on library reserve

Recent Instructors

Paul M. Stevenson, Fall 2007

All information is representative only, and is likely to change from year to year.