Analytical Mechanics

This course introduces fundamental concepts of analytical mechanics. Newtonian Mechanics: Motion with non-constant acceleration; Potential energy and conservative force; Conservative forces in three dimensions; Small oscillations; Coupled oscillators; Central forces; Orbits and Trajectories; Scattering. Collision in center of mass coordinates. Rotating Systems: Rotating coordinate systems; Coriolis forces and Centrifugal forces; Focault Pendulum; Rigid body rotation; inertia tensor, principal axes of inertia, precession. Lagrangian mechanics: calculus of variations; action integral; Hamilton?s principle of least action; generalised coordinates; Hamilton?s equations; Canonical transformations; Liouville?s theorem; Symmetries and conservation laws.