Classical Mechanics

At the end of this course, the students will demonstrate an understanding of the following concepts, procedures and principles of mechanics through the solution of problems related to and or using:

• Newton's laws of motion: mass, force, inertial versus non-inertial reference frames
• Vectors and vector-valued functions in two- and three-dimensions: Cartesian, Polar, Cylindrical and Spherical coordinates systems
• Projectile motion with linear and quadratic drag
• Motion of a charged particle in a magnetic field
• Conservation of momentum and angular momentum, centre of mass, moment of inertia
• Conservation of energy: kinetic energy and work, potential energy, potentials and conservative forces
• Two body central force problems: central forces, Kepler's laws, equations of motion, equations of orbits  
• Oscillations: Hooke's Law, Simple Harmonic Motion, driven damped oscillations, resonance
• Coupled Oscillators: equations of motion and matrix notation, normal modes
• Rotational motion of rigid bodies: total momentum, angular momentum, kinetic energy and potential energy of the centre of mass
• Mechanics in non-inertial reference frames: Newton's Laws in rotating and non-rotating frames, centrifugal forces, Coriolis force, Tides and the Foucault pendulum
• Lagrangian mechanics: review of calculus of variations, Euler-Lagrange equations, Lagrange's equations of motion, Hamilton's principle, generalized coordinates (optional), Lagrange multipliers and constraints, Symmetries and Conservation Laws,  Noether's Theorem (optional)
• Hamiltonian mechanics: the Hamiltonian, Hamilton's equations of motion