Mechanics 1

Mathematics, First Cycle
3 year
Hours per week – 1. semester:

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

Content (Syllabus outline)

Point kinematics: Definitions of basic kinematic variables. Kinematics in curvilinear coordinate systems, polar, cylindrical and spherical coordinate systems. Differential geometry of curves, intrinsic coordinates.
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.

Objectives and competences

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

Intended learning outcomes

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.

Learning and teaching methods

Lectures, exercises, consultations


2 midterm exams instead of written exam, written exam
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

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]