## Babes-Bolyai University of Cluj-Napoca Faculty of Mathematics and Computer Science Study Cycle: Graduate SUBJECT

 Code Subject MMM0003 Analytical Mechanics
 Section Semester Hours: C+S+L Category Type Mathematics - in RomanianMathematics - in Hungarian 6 2+1+0 speciality optional Mathematics-Computer Science - in Hungarian 6 2+1+0 speciality optional Applied Mathematics 6 2+1+0 speciality optional
 Teaching Staff in Charge
 Lect. GROSAN Teodor, Ph.D.,  tgrosanmath.ubbcluj.roAssoc.Prof. SZENKOVITS Ferenc, Ph.D.,  fszenkomath.ubbcluj.roLect. MAKO Zoltan, Ph.D.,  zmakomath.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 -The equation of d'Alembert and Lagrange. Applications: -Equations for the motion of rigid bodies. -The principle of virtual displacements. Applications -Lagrange's equations of the first kind -Lagrange equations of the second kind. Prime integrals. Applications 2. Mechanics of nonholonomic systems -Lagrange's equations of the second kind with multipliers 3. Hamiltonean mechanics: -Theory of Hamilton's equations. Prime integrals -Theory of Hamilton and Jacobi. Applications 4. The stability theory: -Equivalent definitions of the stable equilibrium -Theorems for stability. -Equations of the small oscillations around a stable equillibrium configuration. -Applications. 5. Variational principles of mechanics -Basic notions of calculus of variations - Hamilton's principle
 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%).
 Links: Syllabus for all subjects Romanian version for this subject Rtf format for this subject