Semester 2 Credit Value: | 10 |
ECTS Credits: | 5.0 |
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To introduce the mathematical methods required for the modelling and description of physical dynamic systems.
Module outline
In mathematics and physics, dynamics is the study of movement and change over time, in ways that can be described by mathematical equations or systems of equations. The aim is to explain and predict past and future patterns using basic principles of mathematics. Objects of interest might be tiny particles or huge stars, there might be a single object or very many.
Working from a mathematical point of view, we will formulate problems in terms of functions which can be differentiated or integrated, so essentially working with ordinary differential equations (ODEs). In modern mathematical usage, ‘dynamics’ describes the analysis of such ODEs. This will involve methods you’ve met (or are meeting) in other modules. We’ll focus on problems of idealised 'point particles' (simple bodies) and describe their motion when they are thrown or shot (ballistic), oscillating or orbiting something (circular and elliptical orbits).
Particle dynamics: differentiation and integration of a vector-valued function; position, velocity and acceleration vectors in Cartesian and polar coordinates.
Newton's laws of motion and energetics: forces and linear momentum; angular momentum; kinetic and potential energies; motion under gravity; variable mass problems.
Spring oscillator and pendulum motion: small amplitude, simple harmonic motion; damped and forced oscillations; large amplitude motion and nonlinear oscillations.
Orbital motion: Newton's law of gravity; equations of orbital motion; Kepler's laws.
Multiple particles: two body system including reduced mass; introduction to N-body case; centre of mass.
Students will know how to describe systems of moving objects through mathematical equations. They will be able to solve these equations to find expressions for characteristics such as future positions and velocity. They will be familiar with laws of motion and the effect on measured characteristics of the relative velocity between object and observer.
Students will be able to integrate and differentiate vector valued functions. They will have enhanced algebraic and mathematical manipulation skills. They will be able to solve problems requiring the mathematical interpretation of physical behaviour.
Category | Activity | Number | Length | Student Hours | Comment |
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Scheduled Learning And Teaching Activities | Lecture | 10 | 1:30 | 15:00 | Formal Lectures synchronous online or Present-in-Person |
Scheduled Learning And Teaching Activities | Lecture | 2 | 1:00 | 2:00 | Revision Lectures – Present in Person |
Scheduled Learning And Teaching Activities | Lecture | 10 | 1:00 | 10:00 | Problem Classes – Present-in-Person |
Guided Independent Study | Assessment preparation and completion | 15 | 1:00 | 15:00 | Completion of in course assessments |
Guided Independent Study | Assessment preparation and completion | 53 | 1:00 | 53:00 | Preparation time for lectures, background reading, coursework review. |
Scheduled Learning And Teaching Activities | Drop-in/surgery | 5 | 1:00 | 5:00 | Office Hour - Present-in-Person |
Total | 100:00 |
Code | Title |
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PHY1020 | Dynamics |
Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem classes are used to help develop the students’ abilities at applying the theory to solving problems.
The format of resits will be determined by the Board of Examiners
Description | Length | Semester | When Set | Percentage | Comment |
---|---|---|---|---|---|
Written Examination | 120 | 2 | A | 80 | N/A |
Module Code | Module Title | Semester | Comment |
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PHY1020 | Dynamics | 2 | N/A |
Description | Semester | When Set | Percentage | Comment |
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Prob solv exercises | 2 | M | 10 | Problem-solving exercises |
Prob solv exercises | 2 | M | 10 | Problem-solving exercises |
A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.
In the event of on-campus examinations not being possible, an on-line alternative assessment will be used for written examination 1.
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Disclaimer: The information contained within the Module Catalogue relates to the 2021/22 academic year. In accordance with University Terms and Conditions, the University makes all reasonable efforts to deliver the modules as described. Modules may be amended on an annual basis to take account of changing staff expertise, developments in the discipline, the requirements of external bodies and partners, and student feedback. Module information for the 2022/23 entry will be published here in early-April 2022. Queries about information in the Module Catalogue should in the first instance be addressed to your School Office.