MODULE TITLE

Analytical and Chaotic Dynamics

 

CREDIT VALUE

15

MODULE CODE

PHY2032

MODULE CONVENER

Dr M.K.M. Browning

 

 

DURATION

TERM

1

2

3

Number Students Taking Module (anticipated)

33

WEEKS

T2:01-11

 

DESCRIPTION – summary of the module content (100 words)

This module introduces some fundamental concepts in analytical dynamics, and illustrates their applications to relevant problems. The module covers the calculus of variations, Lagrangian and Hamiltonian formulations of dynamics, Poisson brackets, canonical transformations, and Hamilton-Jacobi equations. The approach is necessarily mathematical and students are advised to take this optional module only if they have got marks of at least 60% in both PHY1021 Vector Mechanics and PHY1026 Mathematics for Physicists (or in equivalent modules in other departments).

MODULE AIMS – intentions of the module

This module will be of interest to students wishing to develop their grasp of theoretical physics. The subject of analytical dynamics provides advanced theoretical developments which prove elegant and versatile in solving dynamical problems.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

 On successful completion of this module you should be able to:

Module Specific Skills and Knowledge:

  1. solve advanced dynamical problems involving classical particles by applying the Lagrangian and Hamiltonian formulations;
  2. explain the calculus of variations and apply it to the solution of problems;
  3. state the Hamilton-Jacobi equations and apply them to the solution of problems;
  4. describe the relationship between poisson brackets and quantum mechanical commutation relations;
  5. describe the basic concepts of chaos theory and explain how chaos theory may be used in different disciplines;

Discipline Specific Skills and Knowledge:

  1. formulate mathematical descriptions of physical systems;

Personal and Key Transferable / Employment Skills and Knowledge:

  1. use mathematics to solve problems.

SYLLABUS PLAN – summary of the structure and academic content of the module

  1. Generalized coordinates. Holonomic and nonholonomic constraints
  2. Virtual displacement. D'Alembert's principle
  3. The Lagrangian formulation
  4. The Hamiltonian formulation
    1. Configuration space; generalized (canonical or conjugate) momentum
    2. Phase space
    3. Legendre transformation
    4. Hamiltonian; Hamilton's equations
    5. Cyclic co-ordinates and conservation theorems
    6. Liouville's theorem
  5. Calculus of variations
  6. Poisson brackets
    1. Lagrange brackets
    2. Poisson brackets
  7. Hamilton-Jacobi equations and action-angle variables
  8. The transition to quantum mechanics
  9. Nonlinear Dynamical Systems
    1. Chaos and its relevance to mechanics
    2. The stability of non-linear equations
    3. The non-linear oscillator
    4. Phase-Space Methods
    5. The pendulum revisited
    6. Mappings
    7. Characterisation of chaotic systems

 

LEARNING AND TEACHING

 

LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)

Scheduled Learning & Teaching activities  

22 hours

Guided independent study  

128 hours

Placement/study abroad

0 hours

 

DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS

 Category 

 Hours of study time 

 Description 

Scheduled Learning & Teaching activities

20 hours

20×1-hour lectures

Scheduled Learning & Teaching activities

2 hours

2×1-hour problems/revision classes

Guided independent study

30 hours

5×6-hour self-study packages

Guided independent study

16 hours

4×4-hour problems sets

Guided independent study

82 hours

Reading, private study and revision

 

ASSESSMENT

 

 FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade

Form of Assessment

Size of the assessment e.g. duration/length

ILOs assessed

Feedback method

Guided self-study

5×6-hour packages

1-7

Discussion in class

4 × Problems sets

4 hours per set

1-7

Solutions discussed in problems classes.

SUMMATIVE ASSESSMENT (% of credit)

Coursework

0%

Written exams

100%

Practical exams

0%

 

DETAILS OF SUMMATIVE ASSESSMENT

Form of Assessment

 

% of credit

Size of the assessment e.g. duration/length

 ILOs assessed 

Feedback method

Final Examination

100%

120 minutes

1-7

Mark via MyExeter, collective feedback via ELE and solutions.

 DETAILS OF RE-ASSESSMENT (where required by referral or deferral)

Original form of assessment

 Form of re-assessment 

ILOs re-assessed

Time scale for re-assessment

Whole module

Written examination (100%)

1-7

August/September assessment period

RE-ASSESSMENT NOTES  

See Physics Assessment Conventions.

 

RESOURCES

 

 INDICATIVE LEARNING RESOURCES -  The following list is offered as an indication of the type & level of information that you are expected to consult. Further guidance will be provided by the Module Convener.

Core text:

Supplementary texts:

ELE:

CREDIT VALUE

15

ECTS VALUE

7.5

PRE-REQUISITE MODULES

Vector Mechanics (PHY1021) and Mathematics for Physicists (PHY1026)

CO-REQUISITE MODULES

none

NQF LEVEL (FHEQ)

5

AVAILABLE AS DISTANCE LEARNING

NO

ORIGIN DATE

01-Feb-12

LAST REVISION DATE

06-Aug-20

KEY WORDS SEARCH

Physics; Equations; Hamilton; Brackets; Dynamical; Poisson; Formulations; Chaos; Hamiltonian; Jacobi; Mechanics.

Module Descriptor Template Revised October 2011