"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science
| Mathematical models in Mechanics. Special topics |
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| Teaching Staff in Charge |
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| Aims |
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The aim of this course is to establish some mathematical models for special topics of theoretical mechanics as the shock (collisions) theory, the mechanics of variable mass systems, the rockets theory etc. Some features connected with the optimal trajectories for the rockets together with the launch of artificial satellites are also envisaged. |
| Content |
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This course is an extension of the classical mechanics which has been the target of the previous course MM001. The analysis of the collisions phenomena which implies the consideration of unbounded forces (represented by temporary distributions) will be followed by establishing of the equations for the variable mass systems, the rockets and the jets being the most known particular cases. Then the Tiolkovski formulas, the Pontriagyne principle allow us an analysis of different optimization procedures for the trajectories of these rockets within the launch of artificial satellites too. |
| References |
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1. Dragos, Lazar: Principiile Mecanicii Analitice, Bucuresti, Ed. Tehica, 1976
2. Iacob, Caius, Mecanica Teoretica, Bucuresti, Editura Didactica si Pedagogica, 1972 3. Turcu, Aurel , Capitole Speciale de Mecanica, vol, 2, Ciocniri. Percutii. Dinamica corpului de masa variabila. Dinamica rachetelor in regim optimal. Problema plana a teoriei elasticitatii, Univ. Babes-Bolyai , Cluj-Napoca, Litogr., 1993. 4. Arnold, Vladimir I., Mathematical Models of Classical Mechanics, Berlin, pringer, 1997 5. Landau, L.D., Lifsit, E.M., Mecanica., Fizica teoretica, Ed. Tehica, Bucuresti, 1966 |
| Assessment |
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Exam 70%, active seminar attendance 30% |