Dynamics - 2019 entry

This module introduces Newtonian dynamics and its applications. You will learn how to use calculus, vectors and matrices for modelling physical man-made and natural systems, and how systems change with time. Starting with moving objects (for example, individual projectiles and pendulums) and energy (balance) equations, you will move onto more complicated problems such as motion of a particle in a potential landscape, damped and driven oscillators, coupled oscillators, and nonlinear dynamics of interacting species (for example, predator-prey models).

Prerequisite modules: “Calculus and Geometry” (ECM1901) and “Vectors and Matrices” (ECM1902) or equivalent.

The aim is to introduce you to Newtonian dynamics and its applications; to apply calculus, vectors and matrices in the modelling of physical man-made and natural systems; to introduce you to applied mathematics as a tool for investigating technology and natural phenomena. As examples, you will explore the consequences of physical laws, as well as the behaviour of physical systems from projectiles and population models.

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:

1 demonstrate an understanding of basic concepts concerning dynamical systems for modelling of physical man-made and natural systems;

2 develop the ability to perform an analysis for different types of dynamical systems to develop solutions, identify equilibria, and characterise stability;

3 apply theoretical knowledge to model mechanical, electrical, and natural example systems.

Discipline Specific Skills and Knowledge:

4 demonstrate a basic knowledge and understanding of fundamental concepts of changing physical systems, using the rate of change (that is differentials) to model real systems, and analyse properties and characteristics of models;

5 synthesize a range of mathematical and computational techniques (in e.g. Python, MATLAB) for basic manipulations of dynamics and dynamical systems.

Personal and Key Transferable / Employment Skills and Knowledge:

6 reason using abstract ideas, formulate and solve problems and communicate reasoning and solutions effectively in writing and oral presentation;

7 work in groups to solve in-depth problems effectively; and learn to analyse/assess other solutions for problems;

8 acquire ability for self-criticism of your work;

9 demonstrate appropriate use of learning resources;

10 demonstrate self-management and time management skills.

- Basics for modelling: space, time, velocity, acceleration, point particles, Newtonian mechanics;

- Dynamic equations of motion: gravity, projectiles, trajectories, envelope of trajectories;

- Simple harmonic motion: elasticity, Hooke's law, strings and springs, equilibria and oscillations, examples: mass-spring dampers, electrical circuits;

- Energy: kinetic energy and gravitational potential energy, elastic potential energy, motion under general potentials, basic variational principles, symmetries and conservation laws, equilibria, stability and attractors;

- Oscillations: damping, forcing and resonance, systems of coupled oscillations, normal coordinates, normal modes;

- Linear systems: higher order systems, general and specific solutions, classification of equilibria;

- Nonlinear systems: first and higher order systems, phase plane, linearisation about equilibria in nonlinear systems, classification of equilibria, chaos, examples: predator-prey models, Lorenz system;

- Planetary motion: motion in plane polar coordinates, velocity and acceleration, central forces and angular momentum.

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.

If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

Basic reading:

ELE: http://vle.exeter.ac.uk/

Other Resources:

Reading list for this module: