# M4: Dynamics - Material for the year 2019-2020

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16 lectures

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.

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.

See the examinable syllabus.

Newton's laws and inertial frames. Dimensional analysis. [1.5]

Forces: examples including gravity, fluid drag, electromagnetism. Energy and momentum. [2.5]

Equilibria and the harmonic oscillator. Stability and instability via linearized equations, normal modes. Simple examples of equilibria in two variables via matrices. [2]

Planar motion in polar coordinates. Conservative forces, central forces, angular momentum and torque. Constrained motion. [3]

Newtonian gravitational potential, Kepler's laws and planetary motion. [2.5]

Many particle systems, centre of mass motion, Galilean relativity. [1.5]

Rigid bodies, the inertia tensor, and simple rigid body motion (with fixed axis of rotation). Newton's laws in rotating frames. [3]

1) David Acheson, *From Calculus to Chaos: an Introduction to Dynamics* (Oxford University Press, 1997), Chapters 1, 5, 6, 10.

2) M. Lunn, *A First Course in Mechanics* (Oxford University Press, 1991), Chapters 1--3, 5, 6, 7 (up to 7.3).

3) M. W. McCall, *Classical Mechanics: A Modern Introduction* (Wiley, 2001), Chapters 1--4, 7.