to introduce students to a range of problems in Newtonian Mechanics, including, principally, the Kepler problem.
by the end of the module students should be able to
- manipulate vectors fluently, including use of scalar and vector products and time-differentiation thereof;
- use these techniques in a range of unseen mathematical problems based on the syllabus below;
- derive results from the syllabus, including Newton’s deduction of Kepler’s laws from the inverse-square law of gravity.
- Vectors (revision): Scalar, vector and triple products; time-derivatives.
- Vector mechanics: Conserved quantities (energy, momentum, angular momentum). Frames of reference and Galilean relativity.
- Rotational motion: Circular motion and angular velocity. Rotating frames and the Coriolis effect. Rigid-body rotations, inertia tensor, moment of inertia. Euler's equations of motion for a rigid body, stability of rotational motion.
- Systems of particles: Centre-of-mass of two- and many-particle systems. Virial theorem (and implications for dark matter). Reduced mass of two particles.
- Newtonian Gravity: Historical background, Kepler's laws. A geometric equation for orbits. Conic sections and relation with energy and angular momentum. Deduction of Kepler's laws. Stability of orbits.
- R Douglas Gregory, Classical Mechanics (Cambridge University Press 2006) - ISBN 0521534097
- P Smith and RC Smith, Mechanics (John Wiley and Sons 1990) - ISBN 0471927376
2 lectures and 1 seminar per week
One and a half hour closed examination taken in week 1 of Spring Term (90%), Coursework (10%)
Brief details: Requires fluency (at Further Mathematics A2 level) with calculus and vectors, and some background in Physics or Mechanics.
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