Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate
SUBJECT
| MMM0001 | Mechanics |
| Teaching Staff in Charge |
Prof. KOHR Mirela, Ph.D., mkohr math.ubbcluj.roAssoc.Prof. SZENKOVITS Ferenc, Ph.D., fszenko math.ubbcluj.roAssoc.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 of mechanics. |
| Content |
|
I. KINEMATICS:
1. Introduction. Fundamental notions. 2. Kinematics of the material point: path, motion equations, the velocity and acceleration of material point. Kinematics in Cartesian coordinates, with respect to the Frenet orthogonal axes, and in curvilinear coordinates. Areolar velocity. 3. Kinematics of the solid rigid body: Euler's angles. Motion's equations. Poisson's formulas. The velocity and accceleration distributions of solid body. The motion of the solid body with a fixed point. The general rigid-body motion. The plane-parallel motion of the rigid body. 4. The relative motion of the material point. The velocity and acceleration distributins. Coriolis' theorem. II. DYNAMICS OF MATERIAL POINTS: 1. The free material point. Principles of Newtonian mechanics. The Newton equation. Equations and general theorems. Virtual work and the force function. Central forces. Newton's problem. 2. The motion of a material point with restrictions: the motion on a fixed curve and on a fixed surface (with or without friction). The mathematical pendulum. 3. Dynamics of the relative motion: the differential equation of the relative motion. III. DYNAMICS OF SYSTEMS AND RIGID BODIES 1. Centre of mass (inertia, gravity). Momentum of inertia. Momentum of inertia with respect to parallel axes and axes which contain a given point. Principal axes and principal moments. Equations and general theorems of dynamics of the systems of material points. Virtual work of the exterior and inner forces. Prime integrals. General teorems for the motion of a material system with respect to the centre of mass. Konig's formulas. Equations and general theorems for the motion about the centre of inertia. 2. Dynamics of rigid body: The motion of the rigid body with a fixed axis. The motion of the rigid body with a fixed point. Kinematical energy and the kinematical torque. Applications to the Lagrange-Poisson case of motion. Cosiderations related to the general motion of a rigid body. |
| References |
|
[1] Kohr, M., Capitole Speciale de Mecanică, Presa Universitară Clujeană, Cluj- Napoca, 2005
[2] Bradeanu, P., Mecanică Teoretică, vol. 1 şi 2, Litografia Universităţii Babeş-Bolyai, Cluj-Napoca, 1988 [3] Iacob, C., Mecanică Teoretică, Editura Didactică şi Pedagogică, Bucureşti, 1980 [4] Dragoş, L., Principiile Mecanicii Analitice, Editura Tehnică, Bucureşti, 1976 [5] Goldstein, H., Classical Mechanics, Reading, MA: Addison-Wessley Publishing Co. (2nd edition), 1980 [6] Turcu, A., Kohr-Ile, M., Culegere de Probleme de Mecanică Teoretică, Litografia Universităţii Babeş-Bolyai, Cluj-Napoca, 1993 [7] Bradeanu, P., Pop, I., Stan, I., Turcu, A., Culegere de Probleme de Mecanică, Litografia Universităţii Babeş-Bolyai, Cluj-Napoca, 1976. [8] Bose, S., Chattoraj, D., Elementary Analytical Mechanics, Alpha Science International Ltd. 2000 [9] Aaron, F.D., Mecanică Analitică, Editura BIC ALL, Bucureşti, 2002. [10] Trîmbiţaş, R.T., Analiză Numerică. O Introducere Bazată pe MATLAB, Presa Universitară Clujeană, 2005. Bibliografie suplimentară: 1. Arnold, V.I., Mathematical Methods of Classical Mechanics, Springer, Berlin, 1997 2. Cooper, R.K., Pellegrini, C., Modern Analytical Mechanics, Kluwer Academic/Plenum Publishers, New York, 1999 3. Torok, J.S., Analytical Mechanics with an Introduction to Dynamical Systems, John Wiley & Sons, Inc., New York, 2000 4. Kittel, C., Knight, W.D., Cursul de Fizică Berkeley, vol. 1: Mecanica, Editura Didactică şi Pedagogică, Bucureşti, 1981 5. Turcu, A., Mecanică Teoretică, I, II, Litografia Universităţii Babeş- Bolyai, Cluj-Napoca, 1972,1976 6. Taylor, J., Classical Mechanics, Palgrave Macmillan, Ney York, 2004 7. Bradeanu, P., Pop, I., Bradeanu D., Probleme şi Exerciţii de Mecanică Teoretică, Editura Tehnică, Bucureşti, 1979 8. Landau, L., Lifchitz, E., Mécanique, Mir, Moscou, 1981 9. Fetter, A.L., Walecka, J.D., Theoretical Mechanics of Particles and Continua, Dover Publications, Inc., New York, 2003 10.Iro, H., A Modern Approach to Classical Mechanics, World Sci., New Jersey, 2002 11.Budo, Á., Mechanika. Tankönyvkiadó, Budapest, 1972 12.Nagy. K., Elméleti Mechanika. Nemzeti Tankönyvkiadó, Budapest, 1993. 13.VÎLCOVICI, V. et al., Mecanica Teoretica, Ed. Tehnica, Bucuresti, 1963. 14.BALAN, St., Culegere de Probleme de Mecanica. Ed. Didactica si Pedabogica, Bucuresti, 1972. |
| Assessment |
|
Exam at the end of semester: 70%
Student activity: 15% Labwork: 15% |
| Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |