M4: Dynamics - Material for the year 2019-2020

2019-2020
Lecturer(s): 
Prof. James Sparks
Course Term: 
Hilary
Course Lecture Information: 

16 lectures

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 Syllabus: 
Course Synopsis: 

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]

Reading List: 

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.