Classical Mechanics

The details

Requisites for this module

BSC G1F3 Mathematics with Physics,

BSC G1F4 Mathematics with Physics (Including Placement Year),

BSC GCF3 Mathematics with Physics (Including Year Abroad)

BSC G1F4 Mathematics with Physics (Including Placement Year),

BSC GCF3 Mathematics with Physics (Including Year Abroad)

This module concerns the general description and analysis of the motion of systems of particles acted on by forces. Assuming a basic familiarity with Newton's laws of motion and their application in simple situations, the students will develop the advanced techniques necessary to study more complicated, multi-particle systems. The students will also consider the beautiful extensions of Newton's equations due to Lagrange and Hamilton, which allow for simplified treatments of many interesting problems and provide the foundation for the modern understanding of dynamics.

Main Topics:

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

2. The Lagrangian formalism.

3. Small oscillations and stability.

4. The motion of rigid bodies.

5. Hamiltonian formalism.

Main Topics:

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

2. The Lagrangian formalism.

3. Small oscillations and stability.

4. The motion of rigid bodies.

5. Hamiltonian formalism.

The aim of the module is to develop an understanding of how Newton's laws of motion can be used to describe the motion of systems of particles and rigid bodies, and how the Lagrangian and Hamiltonian approaches allow use of more general coordinates systems to simplify treatments of many interesting problems in physics and sciences.

On completion of the module, students should be able to:

* model simple mechanical systems, usingNewton's laws of motion and Lagrange's equations;

* analyse the dynamics of systems near equilibrium (small oscillations and stability);

* relate the Hamiltonian and Lagrangian approaches;

* recognise and make use of conserved quantities;

* find the Euler-Lagrange equations associated with simple problems;

* have an understanding of Liouville's theorem, PoincarĂ©'s recurrence theorem, poisson brackets and canonical transformations.

* model simple mechanical systems, usingNewton's laws of motion and Lagrange's equations;

* analyse the dynamics of systems near equilibrium (small oscillations and stability);

* relate the Hamiltonian and Lagrangian approaches;

* recognise and make use of conserved quantities;

* find the Euler-Lagrange equations associated with simple problems;

* have an understanding of Liouville's theorem, PoincarĂ©'s recurrence theorem, poisson brackets and canonical transformations.

Syllabus:

1. 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.

2. The Lagrangian formalism

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

3. Small oscillations and stability

Simple harmonic oscillations; stability; double pendulum.

4. The motion of rigid bodies

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

5. Hamiltonian formalism

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

1. 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.

2. The Lagrangian formalism

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

3. Small oscillations and stability

Simple harmonic oscillations; stability; double pendulum.

4. The motion of rigid bodies

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

5. Hamiltonian formalism

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

Teaching will be delivered in a way that blends face-to-face classes, for those students that can be present on campus, with a range of online lectures, teaching, learning and collaborative support.

- R. Douglas Gregory. (2006)
*Classical Mechanics*, Cambridge: Cambridge University Press.

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.

Coursework / exam | Description | Deadline | Weighting |
---|---|---|---|

Coursework | Test | ||

Exam | 120 minutes during Summer (Main Period) (Main) |

Coursework | Exam |
---|---|

10% | 90% |

Coursework | Exam |
---|---|

10% | 90% |

Module supervisor and teaching staff

Availability

No external examiner information available for this module.

Resources

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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