Analytical Mechanics

The details
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Undergraduate: Level 5
Monday 13 January 2025
Friday 21 March 2025
22 May 2024


Requisites for this module
MA101 and MA105 and MA114
MA202 and MA210



Key module for

BSC G1F3 Mathematics with Physics,
BSC G1F4 Mathematics with Physics (Including Placement Year),
BSC G1F5 Mathematics with Physics (Including Foundation Year),
BSC GCF3 Mathematics with Physics (Including Year Abroad)

Module description

This module introduces general concepts and methods for the description and analysis of the motion and dynamics of particles, systems of particles, rigid bodies, and fields.

Assuming a basic knowledge of Newtonian mechanics, students will develop advanced techniques necessary to study more complicated, multi-particle systems and rigid bodies. The central part of the module is the Lagrangian and Hamiltonian formulation of Classical Mechanics, which allow for simplified treatments of many interesting problems and provide the foundation for the modern understanding of dynamics.

Module aims

The aims of this module are:

  • To introduce students to the analytical foundations of Classical mechanics (Newtonian, Lagrangian and Hamiltonian mechanics).

  • To introduce students to small oscillations and their stability.

  • To introduce students to symmetries and conserved quantities.

  • To introduce students to the kinematics of rigid bodies.

Module learning outcomes

By the end of this module, students will be expected to be able to:

  1. Demonstrate knowledge and understanding of Newtonian mechanics.

  2. Demonstrate knowledge and understanding of the Lagrangian formalism of classical mechanics.

  3. Identify and solve the Lagrangian equations associated with simple problems.

  4. Demonstrate understanding of the concept of symmetries and conserved quantities, identify and make use of them.

  5. Demonstrate ability to use a range of established techniques and a commensurate level of skills in solving problems relating to dynamics of particles and rigid bodies.

  6. Demonstrate knowledge and understanding of the Hamiltonian formalism of classical mechanics.

  7. Identify and compute Hamilton’s equations of motion associated with simple problems, compute Poisson brackets and work with canonical transformations.

Module information

Indicative Syllabus

Newton's laws of motion (single particles and systems of many particles).

  • Kinematics and dynamics of particles and systems of particles; review of Newton's laws of motion; angular momentum; conservation laws; energy; momentum; examples.

The Lagrangian formalism

  • The principle of least action; changing coordinate systems; constraints and generalised coordinates; Noether's theorem and symmetries; examples.

Small oscillations and stability

  • Simple harmonic oscillations; stability; double pendulum.

The motion of rigid bodies

  • Kinematics; inertia tensor; Euler's equations; free tops; Euler's angles; examples.

Hamiltonian formalism

  • Hamilton's equations; the Legendre transform; conservation laws; Liouville's theorem; Poincaré's recurrence theorem; Poisson brackets; canonical transformations; examples.

Learning and teaching methods

Teaching in the School will be delivered using a range of face-to-face lectures, classes, and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.


The above list is indicative of the essential reading for the course.
The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students.
Further reading can be obtained from this module's reading list.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Coursework weighting
Coursework   Test     
Exam  Main exam: In-Person, Open Book (Restricted), 120 minutes during Summer (Main Period) 
Exam  Reassessment Main exam: In-Person, Open Book (Restricted), 120 minutes during September (Reassessment Period) 

Exam format definitions

  • Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
  • In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
  • In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
  • In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary, for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.

Your department will provide further guidance before your exams.

Overall assessment

Coursework Exam
10% 90%


Coursework Exam
10% 90%
Module supervisor and teaching staff
Dr Nikolaos Fytas, email:
Dr Nikolaos Fytas



External examiner

Prof Stephen Langdon
Brunel University London
Available via Moodle
Of 35 hours, 31 (88.6%) hours available to students:
2 hours not recorded due to service coverage or fault;
2 hours not recorded due to opt-out by lecturer(s), module, or event type.


Further information

* Please note: due to differing publication schedules, items marked with an asterisk (*) base their information upon the previous academic year.

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