"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Theoretical mechanics (2)
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MM002
5
2+1+0
6
compulsory
Matematică
MM002
7
2+1+0
6
optional
Matematică-Informatică
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 governing 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. The stability theory:
-Equivalent definitions for the stable equilibrium
-Theorems of stability
-Equations describing small oscillations around the stable equilibrium position
-Applications.
5. Variational principles of mechanics

References
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.
Assessment
Exam.