MAU22S04: Mechanics (Hilary Term 2019)

Course content and assessment

80% two-hour written examination.

20% continuously assessed assignments throughout the semester.

Module Prerequisite

MAU22S01

Lectures & Tutorials Info

Lectures: Thurs. 10am (EELT2), Thurs. 1pm (Jol4), Thurs. 4pm (Jol4)

Tutorials: Wed. 5pm (LB04), Fri 12noon (EELT2)

Your tutor: Stephen O'Brien

UPDATE: Lectures instead of tutorials in the week 8 --- (March 25th, 2019):

Additional lecture: Wed. 20 March 2019: 5pm (LB04) or Fri. 22 March 1019: 12noon (EELT2).

Note: the same lecture will be given twice, so it is enough to visit only one slot corresponding to your scheduled tutorial time.

Tutorials on Friday, 29 March 2019, 12 noon, on Energy Diagrams will be given by Aideen Griffin.

Module Content (this is a provisional syllabus)

  • Introduction
  • Scalar and vector products, differentiation and integration of vectors, velocity and acceleration, Newton's Laws.

  • Motion in Plane Polar Coordinates
  • Derivation of velocity and acceleration in polar coordinates and applications to circular and elliptical motion of a particle.

  • Central Force Motion
  • Equations of motion for a particle in a central force field, derivation of the orbit equation, conservation of angular momentum, potential energy, conservation of energy, solution of the orbit equation for different force fields, apsides and apsidal angles, calculation of maximum and minimum distance of a particle from the origin of a force, inverse square law of attraction and conic sections, properties of the ellipse. Planetary motion, Newton's Universal Law of Gravitation, proof of Kepler's Laws, examples involving calculating eccentricity, periodic time, velocity at aphelion and perihelion of planets and related problems.

  • Work and Energy
  • Evaluation of work done by a force on a particle using line integrals, work as related to kinetic and potential energy, conservative forces, path independence, conservation of energy. Energy diagrams -- use of energy diagrams to analyse the motion of a particle qualitatively, positions of stable and unstable equilibrium, small oscillations in a bound system.

  • Lagrangian and Hamiltonian Mechanics
  • Generalised coordinates, Lagrangian and the action of the system, Hamilton's principle, derivation of Euler-Lagrange equation and some applications. Generalised forces and generalised momenta. Hamiltonian and Hamilton's equations.

    Selected Tutorials

    1. Tutorial 1: Examples 1.5. and 1.6. from Kleppner's book (review of operations with vectors) and Example 1.8. discussing the uniform circular motion.
    2. Tutorial 2 - page1 Tutorial 2 - page2 and Example 1.8. on pages 33-35 in Kleppner-Kolenkow book on the Acrhimedean Spiral.
    3. Tutorial 3 - page1 Tutorial 3 - page2 Tutorial 3 - page3
    4. Tutorial 4 - page1 Tutorial 4 - page2 Tutorial 4 - page3 Tutorial 4 - page4 Tutorial 4 - page5
    5. Tutorial 5 - problems Tutorial5 - solutions
    6. Tutorial 6 - page1 Tutorial 6 - page2
    7. Tutorial7 - problems and solutions
    8. Tutorial8 - problems and solutions
    9. Tutorial 9 - problems Tutorial9 - solutions