School of Computing and Mathematics

Faculty of Natural Sciences

For academic year: 2019/20 Last Updated: 11 November 2019

MAT-20005 - Dynamics

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The module is an introduction to dynamics with applications mainly to systems which can be modelled by particle dynamics. The topics investigated include: Newton's laws, momentum, kinetic and potential energy, projectiles, simple harmonic motion, springs, the pendulum, rocket motion, planetary and satellite orbits, linear theory of oscillations, and normal modes.

The module develops the following Keele Graduate Attributes:

1. an open and questioning approach to ideas, demonstrating curiosity and independence of thought;

2. an appreciation of the development and value of Mathematics, and the links between different areas of the subject;

4. the ability creatively to solve problems using a range of different approaches and techniques, and to determine which techniques are appropriate for the problem at hand;

6. the ability to communicate clearly and effectively in written form.

The module develops the following Keele Graduate Attributes:

1. an open and questioning approach to ideas, demonstrating curiosity and independence of thought;

2. an appreciation of the development and value of Mathematics, and the links between different areas of the subject;

4. the ability creatively to solve problems using a range of different approaches and techniques, and to determine which techniques are appropriate for the problem at hand;

6. the ability to communicate clearly and effectively in written form.

The aim of this module is to demonstrate the successful application of mathematics in the modelling of physical systems, within the context of Newtonian dynamics.

solve problems in kinematics by calculating velocity and acceleration;: solve problems involving central forces and model planetary motion, the motion of satellites and orbital transfer: 1,2,3

apply Newton's Laws of Motion in a number of different contexts;: interpret a system's dynamics from the energy equation: 1,3

model and solve problems involving vertical motion under gravity and projectiles, with or without air resistance;: consider the effect of variable mass via the "rocket equation: 1,2,3

solve problems involving oscillations of springs with or without frictional damping and/or forcing, and be able to recognise the phenomenon of resonance:

apply Newton's Laws of Motion in a number of different contexts;: interpret a system's dynamics from the energy equation: 1,3

model and solve problems involving vertical motion under gravity and projectiles, with or without air resistance;: consider the effect of variable mass via the "rocket equation: 1,2,3

solve problems involving oscillations of springs with or without frictional damping and/or forcing, and be able to recognise the phenomenon of resonance:

Lectures: 35 hours

Formative Class Test: 1 hour

Examples Classes: 12 hours

Independent study: 100 hours

Unseen examination: 2 hours

Formative Class Test: 1 hour

Examples Classes: 12 hours

Independent study: 100 hours

Unseen examination: 2 hours

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Approximately 3 assignments set at regular intervals

Continuous assessment consists of approximately three written problem sheets. The solutions to each problem sheet should consist of approximately four to six handwritten pages.

Mid-semester class test

A class test lasting approximately 40 mins and covering material from approximately the first half of the module.

2-hour end of semester examination

The examination paper will consist of no less than five and not more than eight questions, all of which are compulsory.