Classical Mechanics

Part 1 Linear motion: Newtonian theory; interactions; the drag racer - frictional force; sport parachuting - viscous force; archery - spring force; methods of solution; simple harmonic oscillator; damped harmonic motion; forced oscillator with damping resonance. Part 2 Energy conservation: potential energy; gravitational escape; small oscillations; three-dimensional motion - vector notation; conservation forces in three dimensions; motion in a plane; simple pendulum; coupled harmonic oscillators. Part 3 Lagrangian method: Lagrange's equations; some Lagrangian applications; the Lorentz force; mechanical constraints; Hamilton's equations. Part 4 Momentum conservation: rocket motion; frames of reference; elastic collisions - laboratory and center-of-mass systems; collisions of billiard balls; inelastic collisions; scattering cross sections. Part 5 Angular-momentum conservation: central forces; planetary motion; eccentricity vector; Kepler's laws; satellites and spacecraft; grand tours of the outer planets; Rutherford scattering. Part 6 Particles systems and rigid bodies: center of mass and the two-body problem; rotational equation of motion; rigid bodies - static equilibrium; statics and dynamics of a heavy string; rotations of rigid bodies; gyroscope effect; the boomerang; moments and produces of intertia; single-axis rotations; moments-of-intertia calculations; impulses and billiard shots; super-ball bounces. Part 7 Accelerated coordinate systems: transformation to moving coordinate frames; fictitious forces; motion on the earth; Foucault's pendulum; dynamical balance of a rigid body; principal axes and Euler's equations; the tennis racket theorem; the earth as a free symmetric top - external observer; spinning top, including gravity; slipping tops - rising and sleeping; the tippie-top. Part 8 Gravitation: attraction of a spherical body - Newton's theorem; the tides; gravity field of the earth. Part 9 Newtonian cosmology: the universe; virial theorem; dark matter; cosmology. Part 10 Non-linear mechanics and the approach to chaos: the anharmonic oscillator; the damped and driven anharmonic oscillator; numerical solutions. Part 11 Relativity: the relativity idea; Lorentz transformation; consequences of relativity; relativistic momentum and energy.