Dynamics and Relativity

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

• recall and apply the concept of the Lagrangian in simple situations
• understand and exploit the conservation laws of momentum and energy for simple situations;
• derive and solve the differential equations arising from Newton’s laws of motion applied to simple situations using vector notation
• understand the concepts of relative velocity and of gravitational and frictional forces
• understand the fundamental concepts of special relativity
• derive key results for time dilation, length contraction and velocity addition at high speed

Vectors:

Revision of vector algebra

General motion: position/velocity/acceleration components

Newtonian kinematics:

Forces and energy

Galilean transformation

Time/space/events/observers

Relative velocity

Special relativity:

Spacetime

Lorentz transformation

Velocity addition

Time dilation/length contraction

Redshift

four-momentum and E=mc2

Newtonian dynamics:

Centre of mass/equilibrium

Newton’s laws

Simple forces: gravity, friction, elasticity

Conservation of mass, linear momentum

Collisions (including relativistic effects)

Rocket motion

Rigid body motion

Cylindrical and spherical polar coordinates

Orbital motion

Analytical dynamics:

The calculus of variations

Lagrangians

The Euler-Lagrange equations

The lecturer will provide a structured week-by-week study programme, based largely on the notes provided. Each week there will be three hours of lectures. There will be a problems class every week, each lasting one hour which will be used to study problems illustrating the lecture material. Students may also attend a workshop each week to gain additional personal help with understanding lecture material or problem sheets. Students should spend their private study time studying the lecture notes and working through these problem sets. Online learning materials are also provided via the a Blackboard website.

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Repeat

An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.