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| MECA0202-1 | Analytical Mechanics II | |||||
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| Duration : | 30h Th, 15h Pr | |||||
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| Holder(s) : | Jean Surdej | |||||
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| Course contents : | The Lagrangian formulation of mechanics is intimately connected to the introduction of generalized coordinates which are used to describe the motion of a system of particles (including the solids) by elimination of possible constraints restricting their movements. We first introduce the Lagranges equations and apply this formalism to several different problems (cf. study of the symmetric top known as the Lagrange-Poisson problem, ). Then, we consider the symmetries of a problem and determine which are the associated quantities that are being preserved, via the application of Noethers theorem. The Hamilton variational problem is also discussed. One of the major interests of the Hamiltonian formulation of the dynamics comes from the importance of this formalism in the elaboration of modern physical theories such as quantum mechanics or to describe the fundamental interactions between particles. Within the latter formalism, we derive the canonical equations of Hamilton and we discuss the importance of the canonical transformations in order to solve various mechanical problems. The equations of dynamics are also expressed in terms of the Poisson brackets. Several applications are considered. Finally, we present the Hamilton-Jacobi method of resolution of differential equations. The chapter covering special relativity starts with a brief description of the difficulties encountered while attempting to interpret various physical experiments at the end of the XIXth century. We then introduce the Lorentz transformations and the space-time of Minkowski. Time dilation and length contraction are being discussed and analyzed in depth. The dynamical equations of a particle are then derived in the framework of special relativity. | |||||
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| Course objective : | The second part of the course of Analytical Mechanics is devoted to the Lagrangian and Hamiltonian formulation of classical mechanics and to an introduction of special relativity. | |||||
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| Prerequisites : | It is being assumed that the first part of the course of Analytical Mechanics is familiar to the students. | |||||
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| Organization : | In principle, the theoretical course begins with the start of the academic year. The lectures last 1h30min and take place on Monday and Thursday mornings at the Institute of Mathematics. The precise dates and location will become known to the students in early September. | |||||
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| Written notes : | One set of lecture notes will be distributed to one student at the beginning of the first lecture. Copies will be made and distributed by this student to all students. Reference books related to the course of Analytical Mechanics (2nd part) are : 1. in French : - R. SIMON, Mécanique analytique, Volume 2 (1988), Editions Derouaux, Liège. - J.W. Leech, Elements de Mécanique Analytique, 1961, Monographies Dunod, Paris. - R. SIMON, Compléments de mécanique analytique, 1987, Editions Derouaux, Liège. 2. in English : - J.W. Leech, Classical Mechanics, 1958, Butler and Tanner Ltd, Frome (printed in Great Britain) - "Theory and Problems of Theoretical Mechanics" par Murray Spiegel (1967, Schaum Publishing Co.). | |||||
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| Assessment : | A written (2 exercises) and an oral exam (2 questions, approximately 2h) will be proposed in January. Evaluation of the students will essentially be based upon his(her) understanding of the theory as opposed to his(her) memory skills. One or two tests will be organized during the academic year. The results of these tests will only have a positive impact on the final note (oral and practical exams) obtained by the student. | |||||
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| Contacts : | J. Surdej (Professor and FNRS honorary research director): surdej@astro.ulg.ac.be Tel.: 04/3669783 M. Jaspers - Van der Rest (chef de travaux) : M.vdRest@ulg.ac.be Tel. : 04/3663664 Mrs Caro (Secretary): caro@astro.ulg.ac.be Institute of Astrophysics and Geophysics, ULg, Allée du 6 Août 17, Bât. B5c, B-4000 Sart Tilman (Liège) - Tel.: 04/366 97 16, Fax: 04-366 97 46 http://www.astro.ulg.ac.be/GRech/AEOS/ http://www.astro.ulg.ac.be/~surdej/student.html | |||||
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ULg : Students and Studies Administration - Academic Affairs
Contact : Monique Marcourt, direction A.E.E.
Date of data : 27/02/2006
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