Mechanics 1

Completed courses Analysis 1, Algebra 1, Physics 1, Analysis 2a and Analysis 2b.

Basic principles of Newtonian mechanics: Galileoian structures and transformations. Principle of the determinisem, Newton's laws. Work, energy, work and energy theorems.
Rectilinear motion: Integrability. Qualitative description. Phase portrait. Periodic motion. Harmonic oscillator, harmonic approximation of the periodic motion.
Reduction to the one degree motion: Central froce motion. Integrability of the central froce motion, reduction to the linear motion. Motion in the gravitational field, Kepler's laws, Binet's formula. Motion without friction along a curve.
System of particles: Center of mass, angular momentum theorem. Two body problem.
Rigid body kinematics: Relative and absolute coordinate systems, angular velocity vector. Rigid motion, decomposition into translation and rotation motion. Euler angles.
Rigid body dynamics: Euler equations of motion. Rotation around a fixed axis. Torque free motion. The heavy symmetric top.

J. M. Knudsen, P. G. Hjorth: Elements of Newtonian Mechanics : Including Nonlinear Dynamics, 3rd edition, Springer, Berlin, 2002.

G. R. Fowles, G. L. Cassiday: Analytical Mechanics, 7th edition, Brooks/Cole, Pacific Grove, 2005.

W. Greiner: Classical Mechanics : Point Particles and Relativity, Springer, New York, 2004.

Mathematical correct presentation of the basic Newtonian mechanics with special attention to connect already acquired mathematical knowledge of students.

Knowledge and understanding: Familiarity and understanding of basic principles of Newtonian mechanics.
Application: Application of basic principles of mechanics to the modellisation of real world problems. Base for further study of mechanics.
Reflection: Interconnection of the already acquired mathematical knowledge within a single course and application of it in the field of Mechanics.
Transferable skills: A global understanding of mathematical methods. Acquiring modellisation skills for real world problems.

Lectures, exercises, consultations

Type (examination, oral, coursework, project):
2 midterm exams instead of written exam, written exam
oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

MEJAK, George. Finite element solution of a model free surface problem by the optimal shape design approach. International journal for numerical methods in engineering, ISSN 0029-5981. [Print ed.], 1997, vol. 40, str. 1525-1550. [COBISS-SI-ID 9983833]
MEJAK, George. Vogalna singularnost torzije kompozitne palice = The corner singularity of composite bars in torsion. Strojniški vestnik, ISSN 0039-2480, 2002, letn. 48, št. 11, str. 571-579. [COBISS-SI-ID 5643291]
MEJAK, George. Optimization of cross-section of hollow prismatic bars in torsion. Communications in numerical methods in engineering, ISSN 1069-8299, 2000, vol. 16, št. 10, str. 687-695. [COBISS-SI-ID 9984089]
KOC, Pino, ŠTOK, Boris. Computer-aided identification of the yield curve of a sheet metal after onset of necking. Computational materials science, ISSN 0927-0256. [Print ed.], 2004, letn. 31, št. 1/2, str. 155-168. [COBISS-SI-ID 7467803]
KOC, Pino, ŠTOK, Boris. Usage of the yield curve in numerical simulations. Strojniški vestnik, ISSN 0039-2480, 2008, letn. 54, št. 12, str. 821-829. [COBISS-SI-ID 10772507]
UREVC, Janez, KOC, Pino, ŠTOK, Boris. Characterization of material parameters used in the mathematical modelling of arc welding and heat treatment processes. Transactions of FAMENA, ISSN 1333-1124, 2011, vol. 35, no. 4, str. 1-14, ilustr. [COBISS-SI-ID 12226587]