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PHY1020 : Dynamics

  • Offered for Year: 2019/20
  • Module Leader(s): Dr Graeme Sarson
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus
Semester 2 Credit Value: 10
ECTS Credits: 5.0


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. In addition to working in normal physical space, solving problems with differential equations (such as Newton's laws), the concept of phase space, which describe all the possible states of a system, is introduced; working in phase space, using geometrical methods, greatly assists in the understanding of dynamical systems.

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.

Pendulum motion and phase-space analysis: small amplitude, simple harmonic motion; damped and forced oscillations; introduction to phase-space analysis; large amplitude motion and nonlinear oscillations; 2D motion, double pendulums, and chaos.

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.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture221:0022:00Formal Lectures
Guided Independent StudyAssessment preparation and completion16:006:00Revision for class test
Guided Independent StudyAssessment preparation and completion113:0013:00Revision for unseen exam
Guided Independent StudyAssessment preparation and completion12:002:00Unseen exam
Scheduled Learning And Teaching ActivitiesLecture11:001:00Assignment laboratory
Scheduled Learning And Teaching ActivitiesLecture11:001:00Class test
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem classes
Scheduled Learning And Teaching ActivitiesDrop-in/surgery31:003:00Tutorials in the lecture room
Scheduled Learning And Teaching ActivitiesDrop-in/surgery120:102:00Office hours
Guided Independent StudyIndependent study117:0017:00Studying, practising and gaining understanding of course material
Guided Independent StudyIndependent study52:0010:00Review of coursework assignments and course test
Guided Independent StudyIndependent study44:0016:00Preparation for coursework assignments
Jointly Taught With
Code Title
Teaching Rationale And Relationship

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. Tutorials are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. In addition, office hours (two per week) will provide an opportunity for more direct contact between individual students and the lecturer: a typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Description Length Semester When Set Percentage Comment
Written Examination1202A80N/A
Written Examination402M10Class test
Exam Pairings
Module Code Module Title Semester Comment
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M10Coursework assignments
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments will consist of one written assignment (approximately 3%), one assignment laboratory (approximately 3%) and two computer based assessments (each approximately 2%). The coursework assignments and the (in class, therefore 40 minute) coursework test 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.

Reading Lists