# ANALYTICAL MECHANICS AND MODELLING - 2021/2

Module code: PHY2073

## Module Overview

The module provides a coherent development of the methods of analytical classical mechanics and their applications for students at FHEQ 5 level. The module develops both the necessary formal background and provides practical experience and examples of several applications that enable the derivation of the equations of motion for a more diverse set of physical systems. The module incorporates an existing computational modelling experience that will support the taught material through the numerical implementation and study of a particular physical system.

### Module provider

Mathematics & Physics

FAUX David (Physics)

### Module cap (Maximum number of students): N/A

Workshop Hours: 22

Independent Learning Hours: 95

Guided Learning: 11

Captured Content: 22

Semester 2

None

## Module content

Indicative content includes:

• Introduction and review: Vector nature of Newton’s Laws, the motions of sytems of interacting particles, conservation laws, Energy and the Minimum Energy Principle, degrees of freedom and constraints, Principle of Virtual Work and D’Alembert’s Principle (with their applications to simple mechanical systems).

• Lagrangian Mechanics: Generalised co-ordinates, velocities and forces, and the derivation of Lagrange’s equation. Applications of the Lagrange equation to projectile motion, pendula, motion and orbital properties in a central potential, motion in a rotating frame and rotational motion, oscillatory systems and normal modes analysis.

• Hamiltonian Mechanics: Generalised momenta, derivation of Hamilton’s equations of motion. Revisit of several of the applications in the Hamiltonian formulation.

## Assessment pattern

Assessment type Unit of assessment Weighting
Coursework COMPUTATIONAL MODELLING PROJECT (INTERIM AND FINAL REPORTS) 30
Examination Online ONLINE (OPEN BOOK) EXAM 70

## Alternative Assessment

Late summer resit examination. Successful completion of Level FHEQ 4 of Physics degree.

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

Familiarity and understanding, via unseen problems, of the content of the course materials and the ability to apply these in a new and unrehearsed situation. To apply computational methods and expertise taught in other courses to develop a methodology and computer code to solve and analyse a physical dynamical system of their choosing, with emphasis on the accuracy and the physical results of the model constructed.

Thus, the summative assessment for this module consists of:

• Online examination of duration 2.0hrs taken over a period of 4.0hrs. The examination comprises a section A of compulsory questions and a section B in which students answer 2 questions from 3 (70%).

• Computational modelling project (30%), comprising an assessed interim report (7.5%) and an assessed final report (22.5%).

Formative assessment

Formative feedback on the lecture-based material will be provided weekly through tutorials.

Feedback

Weekly interactive meetings take place in the computational laboratories with feedback on methods and the science. Tutorial support and feedback on progress on examples sheets will be provided as part of the timetable.

## Module aims

• review the vector-based mechanics of Newton and disuss the role of conservation laws
• provide a coherent development, via the Minimum Energy, Virtual Work and D'Alembert Principles, of the physical basis and application of the Lagrangian and Hamiltonian formulations of classical dynamical systems and their solution.
• by the use of examples and selected applications, develop a familarity and a working knowledge of the appropriate choice of generalised coordinates and of constructing the Lagrangian and Hamitonian equations of motion for e.g. linear and rotational motion.
• via the computational modelling component of the module, give a practical experience of the numerical implementation and the solution of a chosen dynamical system.

## Learning outcomes

 Attributes Developed 1 State, derive and use the Minimum Energy, Virtual Work and D'Alembert Principles to solve introductory problems in classical mechanics KCT 2 State Lagrange's and Hamilton’s equations of motion (K). Be able to choose a suitable of generalised coordinates and construct the Lagrangian and Hamiltonian for a range of dynamical systems, and so derive the relevant equations of motion KCT 3 Code, solve and study a computational model of a chosen dynamical system KCPT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to:

Support the practical, problem solving and computational applications of the methods by the provision of a coherent series of lectures that develop the physical basis and derive the formal methods that underpin the (differential) equations of motion of Lagrange and Hamilton.

The learning and teaching methods include:

• Lectures and tutorial periods (30 hours) to introduce the mathematical and formal methods and to practice the application of these methods to model systems in a supported tutorial environment.

• Computational laboratory sessions (20 hours) for the conduct of an individual project that is designed to reinforce to major concepts of the lecture course.

• 70hrs of personal study

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Upon accessing the reading list, please search for the module using the module code: PHY2073

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Physics with Quantum Technologies BSc (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Physics BSc (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Physics with Quantum Technologies MPhys 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Physics MPhys 2 Optional A weighted aggregate mark of 40% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2021/2 academic year.