Theoretical mechanics (2) 
ter 

Teaching Staff in Charge 
Assoc.Prof. KOHR Mirela, Ph.D., mkohr@math.ubbcluj.ro Lect. SZENKOVITS Ferenc, Ph.D., fszenko@math.ubbcluj.ro Lect. BLAGA Cristina Olivia, Ph.D., cpblaga@math.ubbcluj.ro 
Aims 
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. The last part of this course is devoted to the variational principles of analytical mechanics.

Content 
1. Lagrangean mechanics:
Restrictions of motion and displacements D'Alembert and Lagrange's equations. Applications: Equations for the motion of rigid bodies. The principle of virtual displacements. Applications Lagrange's equations of the first and second kind 2. Lagrange's equations with multipliers. 3. Hamiltonean mechanics: Theory of Hamilton's equations. Prime integrals Theory of Hamilton and Jacobi 4. Variational principles of mechanics 5. The stability theory: Equivalent definitions for the stable equilibrium Theorems of stability Equations describing small oscillations around the stable equilibrium position Applications. 
References 
1. P. Bradeanu, Mecanica Teoretica, vol. 2, Lito. Univ. BabesBolyai, 1988.
2. P. Choquard, Mecanique Analytique, vol.12, 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. BabesBolyai, ClujNapoca, 1972, 1976. 9. A. Turcu, M. KohrIle, Culegere de Probleme de Mecanica Teoretica, Lito. Univ. Babes Bolyai, ClujNapoca, 1993. 10.N.M.J. Woodhouse, Introduction to Analytical Dynamics, Oxford Univ. Press, 1987. 
Assessment 
Exam. 