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| MECA0448-1 | Mechanics
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| Duration : | 40h Th, 40h Pr |
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| Holder(s) : | Pierre Dauby, Jean Surdej |
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| Language : | Langue française |
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| Course contents : | The course in Mechanics is divided into four parts. The first is kinematics, which consists in the study of motion independently of its causes (geometrical point of view). The object of dynamics is the relation between the motion of a body and the forces acting on this body. The second part of the course is devoted to the study of the dynamics of particles. The Newton's laws are presented, as well as the conservation principles. Several examples are then discussed: simple and forced harmonic oscillator, non linear forced oscillations (subharmonic and chaotic responses), pendulum, planetray motions (Kepler problem). The laws of mechanics in non inertial frames are then introduced and used to study the Foucault pendulum. In the third part of the course, the dynamics of systems of particles, and the dynamics of solids, are presented. As applications, the Euler-Poinsot problem is studied and the motion of spinning tops is analysed. Finally, in the last part we present the Lagrangian formulation of mechanics. The latter is intimately related 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 motions.
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. |
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| Course objective : | Mechanics is a physical theory describing the motions of bodies in space. The objective of Mechancis is first to introduce the basic notions (inertial frames, force,...) and principles (the Newton's laws, lagrangian mechanics) of the theory. Several mechanical phenomena are then studied in the framework of this theory. Futhermore, Newtonian Mechanics provides a quite appropriate application field for many mathematical notions and allows to illustrate the fundamental role played by mathematics in physical theories. |
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| Prerequisites : | A good knowledge of vector algebra and elementary calculus and geometry is essential. |
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| Workshops : | Practical exercices referring to the course of Analytical Mechanics will begin several weeks after the beginning of the theoretical course. They will take place during a series of 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 : | The course spans over the two terms. The time table for the lectures and for the exercises will be available at the beginning of the academic year. |
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| Written notes : | Lecture notes and copies of transparencies will be provided. |
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| Assessment : | Several tests on exercises are organised. A partial exam can be organised at the end of the first term. Both a written exam on exercises and an oral exam on theory must be taken (40% and 60% of the final grade respectively). |
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| Contacts : | Pierre C. DAUBY, Chargé de cours
Institut de Physique (local 2/57), Bât. B5a, Allée du 6 août 17, B-4000 Liège 1
Tél. : 04/366.23.57
Courriel: PC.Dauby@ulg.ac.be
www : http://www.ulg.ac.be/thermoir/Mecanique_Analytique.htm (http://www.ulg.ac.be/thermoir/%20Mecanique_Analytique.htm)
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, WWW: http://www.astro.ulg.ac.be/~surdej/ |
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| Remarks : | None. |
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