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| MECA0202-2 | Analytical Mechanics II | |||||
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| Duration : | 30h Th, 30h 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 Lagrange's equations and apply this formalism to several different problems (cf. study of the symmetric top known as the Lagrange-Poisson problem, etc.). Then, we consider the symmetries of a problem and determine which are the associated quantities that are being preserved, via the application of Noether's 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. A brief introduction to tensor calculus will be given, namely to possibly use those tools in General Relativity, Cosmology and/or Fluid Mechanics which are courses being taught within the master in space sciences. | |||||
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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. A brief introduction to tensor calculus will also be presented. | |||||
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| Prerequisites : | It is being assumed that the course of Analytical Mechanics I is familiar to the students. | |||||
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| Workshops : | Practical exercices referring to the second part of the course of Analytical Mechanics will begin several weeks after the beginning of the theoretical course. They will take place during several after-noons according to a timetable that will be distributed in september. As far as possible, the physical principles presented during the theoretical courses will be illustrated by numerous examples selected for their importance in physics and in astronomy. | |||||
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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 the students before the beginning of the lectures. Reference books related to the course of Analytical Mechanics (2nd part) are (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. (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. Evaluation of the students will essentially be based upon his(her) understanding of the theory as opposed to his(her) memory skills. One test will be organized during the academic year. The results of this test will only be taken into account if it has a positive (no negative) 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). Institute of Astrophysics and Geophysics, ULg, Allée du 6 Août 17, Bât. B5c, B-4000 Sart Tilman (Liège), Tel.: 04/366 97 83, Fax: 04-366 97 46, E-mail : surdej@astro.ulg.ac.be, Marie Jaspers - Van der Rest, Chef de Travaux. BAT. B5 Mécan.des fluides géophys.- Dyn.des phén.irrév. Allée du 6 Août, 17 (Bât. B5) , 4000 Liège Tél. : 04/3663664 - E-mail : M.vdRest@ulg.ac.be Mrs Caro (Secretary): caro@astro.ulg.ac.be | |||||
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ULg : Students and Studies Administration - Academic Affairs
Contact : Monique Marcourt, direction A.E.E.
Date of data : 18/05/2007
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