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| MECA0479-1 | Analytical Mechanics I
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| Duration : | 30h Th, 30h Pr |
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| Holder(s) : | Pierre Dauby |
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| Language : | French language |
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| Course contents : | Analytical Mechanics I is divided into three 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. Finally, in the last 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. |
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| Course objective : | Newtonian Mechanics is a physical theory describing the motions of bodies in space. The objective of Analytical Mechancis I is first to introduce the basic notions (inertial frames, force,...) and principles (the Newton's laws) of the theory. Several mechanical phenomena are then studied in the frame 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 : | Workshops consist in solving exercices. |
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| Organization : | The course takes place in the first term. The time table for the lectures and for the exercices is availlable in the beginning of the academic year. |
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| Written notes : | Notes and electronic slides can be provided. |
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| Assessment : | Tests on exercices can be organised. Written exam on exercices and oral exam on theory (40% and 60% of the final grade respectively). |
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