MPhys Physics with Theoretical Physics / Course details

Advanced Dynamics

Desirable/Complementary Content:

• Mathematics 2 PHYS10372 
• Vibrations & Waves PHYS10302

To enhance knowledge and understanding of classical mechanics and relativity.

On successful completion of PHYS10672, a student 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 - Syllabus and literature will be provided.

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).