MSP1804
Dynamics
- Offered for Year: 2025/26
- Module Leader(s): Dr Gerasimos Rigopoulos
- Owning School: School of Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
Semesters
Your programme is made up of credits, the total differs on programme to programme.
| Semester 2 Credit Value: | 10 |
| ECTS Credits: | 5.0 |
Aims
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).
Outline Of Syllabus
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.
Learning Outcomes
Intended Knowledge Outcomes
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.
Intended Skill Outcomes
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.
Students will develop skills across the cognitive domain (Bloom’s taxonomy, 2001 revised edition): remember, understand, analyse, evaluate and create.
Teaching Methods
Teaching Activities
| Category | Activity | Number | Length | Student Hours | Comment |
|---|---|---|---|---|---|
| Scheduled Learning And Teaching Activities | Lecture | 10 | 2:00 | 20:00 | Formal Double Lectures |
| Scheduled Learning And Teaching Activities | Lecture | 1 | 2:00 | 2:00 | Revision Double Lecture |
| Scheduled Learning And Teaching Activities | Lecture | 10 | 1:00 | 10:00 | Problem Classes |
| 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 |
| Totals | 100 |
Teaching Rationale And Relationship
The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking. 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.
Assessment Methods
The format of resits will be determined by the Board of Examiners.
Exams
| Component | Length (mins) | Semester | When set | Percentage | Comment |
|---|---|---|---|---|---|
| Written Examination 1 | 120 | 2 | A | 85 | N/A |
Other Assessments
| Component | Semester | When set | Percentage | Comment |
|---|---|---|---|---|
| Prob solv exercises 1 | 2 | M | 5 | Problem-solving exercises assessment |
| Prob solv exercises 2 | 2 | M | 5 | Problem-solving exercises assessment |
| Prob solv exercises 3 | 2 | M | 5 | Problem-solving exercises assessment |
Formative Assessments
| Component | Semester | When set | Comment |
|---|---|---|---|
| Prob solv exercises 1 | 2 | M | Problem-solving exercises assessment |
Assessment Rationale And Relationship
A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of the programme accreditation.
Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.
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.
Timetable
- Timetable Website: www.ncl.ac.uk/timetable/