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

Theoretical mechanics (1)
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MM001
4
2+2+0
6
compulsory
Matematică
MM001
6
2+2+0
5
compulsory
Matematică-Informatică
MM001
6
2+2+0
6
optional
Matematica Economica
Teaching Staff in Charge
Prof. POP Ioan, Ph.D., popi@math.ubbcluj.ro
Lect. SZENKOVITS Ferenc, Ph.D., fszenko@math.ubbcluj.ro
Lect. BLAGA Cristina Olivia, Ph.D., cpblaga@math.ubbcluj.ro
Aims
Teaching of fundamental notions of mechanics: the vector theory and their momentum, cinematics of the material point and of rigid body, fundamental notions from the dynamics of the material point and of the rigid body. Application and profound study of differential and integral calculus theory and also the theory of ordinary differential equations.
Content
I. KINEMATICS:
1. Introduction. The torque of a vector with respect to a point and an axis, respectively.
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.
2. Kinematics of the solid rigid body: Eule's angles. Motion 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. The motion relative to the ground.
III. DYNAMICS OF SYSTEMS AND RIGID BODIES
1. Centre of inertia (gravity). Momentum of inertia. Momentum of inertia with respect to parallel axes and axes which contain a given point. Ellipsoid of inertia (principal axes and directions). Equations and general theorems for the systems of material points. Virtual work of the exterior and inner forces. Prime integrals. The motion of a material system with respect to the centre of inertia. Konig's theorems. Equations and general theorems for the motion about the centre of inertia.
2. Dynamics of the rigid body. The motion of the rigid body with a fixed point. Kinematical energy and the kinematical torque. Applications to the Lagrange case of motion.
IV. ANALYTICAL MECHANICS:
1. Equations of Lagrange. Prime integrals.
2. Equations of Hamilton.


References
1. Bradeanu, P. - Curs de mecanica teoretica, 1 Lit. Univ.,1984
2. Bradeanu, P., Pop, I., Bradeanu, D. - Probleme si exercitii de mecanica teoretica, Ed. Tehnica, Bucuresti, 1979.
3. Turcu, A. - Mecanica teoretica, p. I,II, Lit. Univ. Cluj, 1972, 1976.
4. Bradeanu, P., Turcu, A., Stan, I., Pop, I. - Culegere de probleme de mecanica teoretica, Lit. Univ. Cluj, 1976.
5. Iacob, C. - Mecanica teoretica, Ed. Did. si Ped., Bucuresti 1972.
6. Vilcovici, V. si altii - Mecanica teoretica, Ed. Tehnica, Bucuresti, 1963.
7. Balan, St. - Culegere de probleme de mecanica, EDP, Bucuresti, 1972.
8. Turcu, A. si Kohr, M.- Culegere de probleme de mecanica teoretica, Lit. Univ. Babes-Bolyai, Cluj-Napoca, 1993.
Assessment
Exam.