BSc Physics with Astrophysics

Advanced Dynamics

To enhance knowledge and understanding of classical mechanics and relativity.

On completion successful students will be able to:

1. apply Newton's theory of gravitation to problems of planetary motion and space travel.
2. use inertial forces to explain motion from the viewpoint of rotating frames of reference.
3. derive the general relation between the angular velocity and angular momentum of a rigid body, and use this to solve problems in rotational dynamics.
4. solve problems in relativistic dynamics using the covariant formalism and energy-momentum four vectors.

1.  Preliminaries (3 Lectures)

Newton’s laws of motion

Linear and angular momentum, force and torque

The two-body system

2.  Gravitation (6 Lectures)

Force fields and potentials

Newtonian gravity

Kepler’s motion in a central force field

Particle orbits as conic sections and Kepler's laws

3. Noninertial Frames of Reference (3 Lectures)

Motion in rotating frames

Centrifugal and coriolis forces

4.  Rigid-Body Motion (6 Lectures)

Angular velocity and angular momentum vectors

Moment-of-inertia tensor

Principal moments of inertia

Euler's equations

Free rotation and stability

Gyroscopes

5. Relativistic Dynamics (6 Lectures)

Principles of special relativity

The covariant formalism

Lorentz transformations and relativistic invariance

Relativistic momentum and energy

Applications to relativistic kinematics

Feedback will be provided via solutions to the problem sheets, which will be made available electronically on Teachweb and Blackboard. More detailed feedback will be provided in the exercise class which are integrated within the 24 lectures.

Barger, V. D. & Olsson, M. G. Classical Mechanics: a Modern Perspective, (McGraw-Hill)

Forshaw, J. & Smith, A. G. Dynamics and Relativity, (Wiley)

Marion, J. B. & Thornton, S. T. Classical Dynamics of Particles and Systems, (Academic)
 

Spiegel, M. R. Schaum’s Outline of Theoretical Mechanics, (McGraw-Hill Book Company).