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| Module Availability |
| Autumn Semester |
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| Assessment Pattern |
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Unit(s) of Assessment
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Weighting Towards Module Mark( %)
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Coursework: Exercises and closed book class tests
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25%
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Examination: Written examination (2 hours).
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75%
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| Module Overview |
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| Prerequisites/Co-requisites |
MAT1009 Classical Dynamics |
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| Module Aims |
To develop the theory and methods of Lagrangian and Hamiltonian Dynamics with emphasis on a analytical and geometrical approach. |
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| Learning Outcomes |
At the end of this course a student should have an understanding of the concepts of
Lagrangian and Hamiltonian systems, some geometric aspects and the role of symmetries. A student should be able to derive the Lagrangian and Hamiltonian equations of motion
of classical (typical) dynamical systems; work with symplectic transformations; identify simple symmetries and conservation laws; apply the Hamiltonian perturbation theory to problems related to celestial mechanics. |
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| Module Content |
Review of basic ideas from classical mechanics; Lagrange equations; Legendre transformations.
Hamiltonian formulation of classical mechanics; symplectic geometry; canonical transformations; Hamiltonian flows.
Symmetries, conservation laws and stability of equilibria.
Applications will include planetary motion, rigid body dynamics and spinning tops. |
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| Methods of Teaching/Learning |
Teaching is lectures, example classes and discussion sessions. Learning takes place through lectures, exercises and supervised tutorials. Reading of selected material, and discussion of this material. |
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| Selected Texts/Journals |
Essential
Jorge V. Jose and Eugene J. Saletan, Classical Dynamics – A Contemporary Approach, Cambridge university Press, (1998).
Further Reading
H. Goldstein, Classical Mechanics, 2ne ed., Addison Wesley (1980).
Tom W. B. Kibble and Frank H. Berkshire, Classical Mechanics, 5th ed., Imperial College Press (2004).
J.E. Marsden and T.S. Ratiu, Introduction to Mechanics and Symmetry, 2nd ed., Springer Verlag (1998). |
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| Last Updated |
04.11.08 |
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