| Mecanică teoretică (2) | Theoretical mechanics (2) |
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(Mathematics) |
| Cadre didactice indrumatoare | Teaching Staff in Charge |
| Conf. Dr. KOHR Mirela, mkohr@math.ubbcluj.ro Lect. Dr. SZENKOVITS Ferenc, fszenko@math.ubbcluj.ro |
| Obiective | Aims |
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Acest curs este o continuare a mecanicii clasice care a facut obiectul cursului anterior MM001. Se vor prezenta principiile generale ale mecanicii analitice (principiul lui D'Alembert-Lagrange si principiul deplasarilor virtuale) si aplicatii ale acestora. Se vor stabili ecuatiile lui Lagrange de speta I si II si se vor da diverse aplicatii. Un capitol aparte il ocupa mecanica hamiltoniana: ecuatii canonice, integrale prime, precum si metode de integrare a sistemului canonic. De asemenea, se prezinta teoria stabilitatii, un accent deosebit punandu-se pe cateva rezultate de stabilitate ale lui Lyapunov, Cetaev si Routh. Ultima parte este dedicata principiilor variationale ale mecanicii analitice.
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This course is a continuation of the classical mechanics which has been the aim of the prerequisite course MM001. It describes the general principles of analytical mechanics (the principle of D'Alembert and Lagrange, and the principle of virtual work), and gives some applications of these principles. Also it establishes the Lagrange equations of the first and second kind. A special part treats the theory of Hamiltonian systems as well as some aspects devoted to the theory of stability, focusing on some stability results of Lyapunov, Cetaev and Routh. The last part of this course is devoted to the variational principles of analytical mechanics.
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1. Mecanica lagrangeeana:
-Legaturi si deplasari -Ecuatia lui D'Alembert si Lagrange. Aplicatii: -Deducerea ecuatiilor fluidelor ideale incompresibile; -Deducerea ecuatiilor de miscare a corpului rigid liber. -Principiul deplasarilor virtuale. Aplicatii -Sisteme olonome. Ecuatiile lui Lagrange -Integrale prime 2. Mecanica sistemelor neolonome: -Ecuatiile lui Lagrange cu multiplicatori -Ecuatiile lui Appell -Aplicatii 3. Mecanica hamiltoniana: -Ecuatii canonice -Integrale prime ale sistemului canonic -Teoria lui Hamilton si Jacobi 4. Teoria sistemului canonic. Teoria ultimului multiplicator 5. Principiile variationale ale mecanicii: -Notiuni de calcul variational -Principiul lui Hamilton -Variatii asincrone. 6. Teoria stabilitatii: -Definitii echivalente ale echilibrului stabil -Teoremele lui Lyapunov si teorema lui Cetaev de stabilitate. -Aplicatii. |
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1. P. Bradeanu, Mecanica Teoretica, vol. 2, Lito. Univ. Babes-Bolyai, 1988.
2. P. Choquard, Mecanique Analytique, vol.1-2, Lausanne, 1992. 3. L. Dragos, Principiile Mecanicii Analitice, Ed. Tehnica, 1976. 4. C. Iacob, Mecanica Teoretica, Editura Didactica si Pedagogica, Bucuresti, 1972. 5. H.G. Kwatny, G.L. Blankenship, Nonlinear Control and Analytical Mechanics. A Computational Approach. Birkhauser Boston, Inc., Boston, MA, 2000. 6. J.J. Moreau, Mecanique Classique, tom. I si II, Masson and Cie, Paris, 1970. 7. J.G. Papastavridis, Tensor Calculus and Analytical Dynamics. A Classical Introduction to Holonomic and Nonoholonomic Tensor Calculus, and its Principal Applications to the Lagrangean Dynamics of Constrained Mechanical Systems, CRC Press, Boca Raton, FL, 1999. 8. A. Turcu, Mecanica Teoretica, vols..I,II, Lit. Univ. Babes-Bolyai, Cluj-Napoca, 1972, 1976. 9. A. Turcu, M. Kohr-Ile, Culegere de Probleme de Mecanica Teoretica, Lito. Univ. Babes- Bolyai, Cluj-Napoca, 1993. 10.N.M.J. Woodhouse, Introduction to Analytical Dynamics, Oxford Univ. Press, 1987. |
| Evaluare | Assessment |
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Examen. |
Exam. |