Course Overview: The subject of dynamics is about how things change with time. A major theme is the modelling of a physical system by differential equations, and one of the highlights involves using the law of gravitation to account for the motion of planets.
Learning Outcomes: Students will be familiar with the laws of motion, including circular and planetary motion. They will know how forces are used and be introduced to stability in a physical system.
Course Synopsis: \(\bullet\) Newton's laws and inertial frames. Dimensional analysis. [1.5]
\(\bullet\) Forces: examples including gravity, fluid drag, electromagnetism. Energy and momentum. [2.5]
\(\bullet\) Equilibria and the harmonic oscillator. Stability and instability via linearized equations, normal modes. Simple examples of equilibria in two variables via matrices. [2]
\(\bullet\) Planar motion in polar coordinates. Conservative forces, central forces, angular momentum and torque. Constrained motion. [3]
\(\bullet\) Newtonian gravitational potential, Kepler's laws and planetary motion. [2.5]
\(\bullet\) Many particle systems, centre of mass motion, Galilean relativity. [1.5]
\(\bullet\) Rigid bodies, the inertia tensor, and simple rigid body motion (with fixed axis of rotation). Newton's laws in rotating frames. [3]
