Dynamics & Relativity

Dynamics & Relativity

DYNAMICS AND RELATIVITY
[Note that this course is omitted from Option (b) of Part IA.]

Familarity with the topics covered in the non-examinable Mechanics course is assumed.

Basic concepts

  • Space and time, frames of reference, Galilean transformations. Newton’s laws. Dimensional analysis. Examples of forces, including gravity, friction and Lorentz. [4]
  • Newtonian dynamics of a single particle
  • Equation of motion in Cartesian and plane polar coordinates. Work, conservative forces and potential energy, motion and the shape of the potential energy function; stable equilibria and small oscillations; effect of damping.
  • Angular velocity, angular momentum, torque.
  • Orbits: the u(θ) equation; escape velocity; Kepler’s laws; stability of orbits; motion in a repulsive potential (Rutherford scattering). Rotating frames: centrifugal and Coriolis forces. *Brief discussion of Foucault pendulum.* [8]

Newtonian dynamics of systems of particles

  • Momentum, angular momentum, energy. Motion relative to the centre of mass; the two body problem. Variable mass problems; the rocket equation. [2]
  • Rigid bodies Moments of inertia, angular momentum and energy of a rigid body. Parallel axis theorem. Simple examples of motion involving both rotation and translation (e.g. rolling). [3]

Special relativity

  • The principle of relativity. Relativity and simultaneity. The invariant interval. Lorentz transformations in (1 + 1)-dimensional spacetime. Time dilation and length contraction. The Minkowski metric for (1 + 1)-dimensional spacetime. Lorentz transformations in (3 + 1) dimensions. 4–vectors and Lorentz invariants. Proper time. 4– velocity and 4–momentum. Conservation of 4–momentum in particle decay. Collisions. The Newtonian limit. [7]

Appropriate books

  • † D. Gregory Classical Mechanics. Cambridge University Press 2006(pdf)
  • G.F.R. Ellis and R.M. Williams Flat and Curved Space-times. Oxford University Press 2000(pdf)
  • A.P. French and M.G. Ebison Introduction to Classical Mechanics. Kluwer 1986(pdf)
  • T.W.B. Kibble and F.H. Berkshire Introduction to Classical Mechanics. Kluwer 1986(pdf)
  • M.A. Lunn A First Course in Mechanics. Oxford University Press 1991
  • P.J. O’Donnell Essential Dynamics and Relativity. CRC Press 2015
  • † W. Rindler Introduction to Special Relativity. Oxford University Press 1991(pdf)
  • E.F. Taylor and J.A. Wheeler Spacetime Physics: introduction to special relativity. Freeman 1992(pdf)
  • David Morin Classical Mechanics(pdf)

Associated Github Page

https://jaircambridge.github.io/Dynamics-Relativity-/

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