1 Newtonian Mechanics of Systems of Particles
Review of Newton’s laws; centre of mass; basic kinematic quantities: momentum, angular momentum and kinetic energy; circular motion; 2-body problem; conservation laws; reduction to centre of mass frame. [5]
2 Lagrangian formulation of mechanics
Lagrange’s equations and their equivalence to Newton’s equations, generalized coordinates; constraints; cyclic variables; examples. [5]
3 Potential wells and oscillations
Particle in a potential well; coupled harmonic oscillators; normal modes; wave equation on a finite string and Fourier modes. [4]
4 Hamiltonian formulation
Hamilton’s equations, equivalence with Lagrangian formulation; equilibria, stability; conserved quantities. [4]
5 Rotating Frames and the Rigid Body
Rotating frames in 2-D; centrifugal and Coriolis forces; moments of inertia, parallel axes theorem. Rotations in 3-D; free rigid body rotation, Euler’s equations. [4]