** **

**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

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