# MAS1902 : Dynamics

• Offered for Year: 2020/21
• Module Leader(s): Dr Cora Uhlemann
• Owning School: Mathematics, Statistics and Physics
• Teaching Location: Newcastle City Campus
##### Semesters
 Semester 2 Credit Value: 10 ECTS Credits: 5

#### 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. 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

Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture01:004:00Present in Person
Scheduled Learning And Teaching ActivitiesLecture51:005:00Synchronous On Line Material
Structured Guided LearningLecture materials181:0018:00Non Synchronous Materials
Guided Independent StudyAssessment preparation and completion151:0015:00N/A
Structured Guided LearningStructured non-synchronous discussion91:009:00
Scheduled Learning And Teaching ActivitiesDrop-in/surgery21:002:00Office Hour or Discussion Board Activity
Guided Independent StudyIndependent study471:0047:00N/A
Total100:00
Code Title
PHY1020Dynamics
##### Teaching Rationale And Relationship

Non-synchronous online materials are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on assessed work. Present-in-person and synchronous online sessions are used to help develop the students’ abilities at applying the theory to solving problems and to identify and resolve specific queries raised by students, and to allow students to receive individual feedback on marked work. Students who cannot attend a present-in-person session will be provided with an alternative activity allowing them to access the learning outcomes of that session. In addition, office hours/discussion board activity 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.

Student should consult their timetable for up-to-date delivery information.

#### Assessment Methods

Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.

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

##### Exam Pairings
Module Code Module Title Semester Comment
PHY1020Dynamics2N/A
##### Other Assessment
Description Semester When Set Percentage Comment
Written exercise2M20N/A
Written exercise2M20N/A
Written exercise2A60Alternative Assessment
##### Assessment Rationale And Relationship

The course assessments 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.