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

Computational mechanics
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MM275
1
2+2+0
9
compulsory
Matematică Computaţională - în limba maghiară
Teaching Staff in Charge
Lect. SZENKOVITS Ferenc, Ph.D., fszenko@math.ubbcluj.ro
Aims
The aim of this course is to give a short introduction in modeling of dynamical systems with a finite number of degrees. Students absolving this course will be able to study dynamical problems using Lagrangian end Hamiltonian formalism. They will be able to study various phenomenon using numerical methods.
Content
I. Mathematical methods for differential equations
1. Models and differential equations
2. Models and mathematical problems
3. Stability and perturbation methods
II. Mathematical methods of classical mechanics
1. Dynamical systems and Newtonian dynamics
2. Lagrangian dynamics
3. Hamiltonoian dynamics and Hamilton–Jacobi Theory
III. Chaotic dynamics, stability and bifurcations
1. Stability diagrams
2. Limit cycles
3. Hopf bifurcation
4. Chaotic motions
IV. Numerical methods for ordinary differential equations
1. Numerical methods for initial-value problems
2. Numerical methods for boundary-value problems
V. Applications
References
1. Arnold, V.I.: Metodele matematice ale mecanicii clasice, Editura Stiintifica si Enciclopedica, Bucuresti, 1980.
2. Bellamo, N., Preziosi, L., Romano, A.: Mechanics and Dunamical Systems with Mathematica, Birkhauser, 2000.
3. Butcher, J. C.: The numerical analysis of ordinary differential equations. John Wiley Sons, 1987.
4. Dragos, L.: Principiile mecanicii analitice, Editura Tehnica, Bucuresti, 1976.
5. Bálint, Érdi: The dynamics of the Solar System, ELTE Eötvöos Kiadó, Budapest, 2001 (Hungarian).
6. Nakamura, S.: Numerical analysis and graphic visualization with Matlab, Prestice Hall PTR, New-Jersey, 1996.
7. Press, W. H., Teukolsky, S. A., Vetterling, W. T., Flannery, B. P.: Numerical Recipies in C, The Art of Scientific Computing, Second Edition, Cambridge University Press, Cambridge, New York, Port-Chester, Melbourne, Sydney, 1992.
8. Szenkovits F., Mako Z., Csillik I., Bálint, A.: Mechanikai rendszerek számítógépes modellezése, Ed. Sapientia, Cluj-Napoca, 2002.
Assessment
Priject - 50% and a practical verification - 50%.