Subject: Theoretical Mechanics (2)	Code: MM002	

Semester	 Hours: C+S+L	Type	 Section	
5	2+1+0	compulsory	Mathematics	
7	2+1+0	optional	Mathematics-Computer Science	

Teaching Staff in Charge	Lect. GROSAN Teodor, Ph.D., tgrosan@math.ubbcluj.ro
Assoc.Prof. SZENKOVITS Ferenc, Ph.D., fszenko@math.ubbcluj.ro
Assoc.Prof. BLAGA Cristina Olivia, Ph.D., cpblaga@math.ubbcluj.ro	
Aims	Teaching of fundamental notions of mechanics: cinematics of the material point and of rigid body, fundamental notions from the dynamics of the material point and of the rigid body. Application of the theory of differential and integral calculus theory and also of the theory of differential equations in the study of some special problems in mechanics	
Content	1. Lagrangean mechanics:
    -Restrictions of motion and displacements 
    -generalized coordinates

2. D'Alembert principle in Lagrange form. 

3. Principle of virtual displacements. Applications 
   
4. Lagrange's equations of the first kind with multiplicators
    
5.  Holonomic systems.
   -Lagrange equations of the second kind.
   -Prime integrals. Applications

6. Hamiltonian mechanics:
    -Canonical equations.
    -Prime integrals for the canonical system

7. Hamilton-Jacobi equation
    -Jacobi's theorem

8. The stability theory:
    -Equivalent definitions of the stable equilibrium
    -Theorems for stability. 
    -Equations of the small oscillations around a stable equillibrium configuration.
    -Applications.

9. Variational principles of mechanics
    -Basic notions of calculus of variations

10. Hamilton's principle. Extensions.

11. Voss principle and Maupertuis Principle

12. Shocks mechanics 
-collision of two body

13. Variable mass body mechanics
-Mescerski's equation

14.Rocket theory
-Tiolkovski's formula

1.Mecanica lagrangeeana: 
-Legaturi si deplasari 
-coordonate generalizate	
Selective References	1. AARON, FRANCISC D.: Mecanica Analitica. Bucuresti: Editura BIC ALL, 2002.
2. ARNOLD, VLADIMIR I.: Mathematical Methods of Classical Mechanics. Berlin: Springer, 1997. 
3. BRADEANU, PETRE: Mecanica Teoretica, vol. 2. Cluj-Napoca: Litografia Univ. Babes-Bolyai, 1984. 
4.CHOQUARD PHILIPPE, Mecanique Analytique, vol.1-2. Lausanne: Presses Polytechniques et Universitaires Romandes, 1992.
5. COOPER, RICHARD K. - PELLEGRINI, CLAUDIO: Modern Analytical Mechanics. New York: Kluwer Academic/Plenum Publishers, 1999. 
6. DRAGOS, LAZAR: Principiile Mecanicii Analitice. Bucuresti: Ed. Tehnica, 1976. 
7. IACOB, CAIUS: Mecanica Teoretica. Bucuresti: Editura Didactica si Pedagogica, 1972. 
8. TOROK, JOSEF. S.: Analytical Mechanics with an Introduction to Dynamical Systems. New York: John Wiley & Sons, Inc., 2000. 
9. TURCU, AUREL - KOHR-ILE, MIRELA: Culegere de Probleme de Mecanica Teoretica. Cluj-Napoca: Litografia Univ. Babes-Bolyai, Cluj-Napoca, 1993. 
10.WOODHOUSE, NICHOLAS M.J.: Introduction to Analytical Dynamics. Oxford: Oxford Univ. Press, 1987.
11. ARNOLD, V.I.:  A mechanika matematikai módszerei, Muszaki Könyvkiadó, Budapest, 1985.
12. BUDÓ Ágoston: Mechanika. Tankönyvkiadó, Budapest, 1972
13. TURCU, A.,Mecanica Teoretica, Vol.3,Mecanica Analitica, Univ."Babes-Bolyai", Cluj-Napoca, litogr., 1981.
14. GÁBOS Z.: Az elméleti fizika alapjai. Dacia Könyvkiadó, Kolozsvár, 1982.
15. GANTMACHER, F.: Lectures in Analytical Mechanics. Mir Publishers, Moscow, 1975.
16. LANDAU, L. D. - LIFSIT, E. M.: Mecanica. Fizica teoretica. Editura Tehnica, Bucuresti, 1966.
17. NAGY Károly: Elméleti mechanika. Nemzeti Tankönyvkiadó, Budapest, 1993.
18. SZENKOVITS Ferenc et alii: Mechanikai rendszerek számítógépes modellezése. Kolozsvár,  Sciencia Kiadó, 2002.
19. SZENKOVITS Ferenc: Analitikus mechanika. Kézirat, 2004. [http://math.ubbcluj.ro/~fszenko/em2]	
Assessment	Exam (70%) + student activity (20%) + test paper (10%)