Mechanics

2022/2023
Programme:
Practical Mathematics
Year:
3 year
Semester:
first
Kind:
mandatory
ECTS:
5
Language:
slovenian
Hours per week – 1. semester:
Lectures
2
Seminar
0
Tutorial
1
Lab
1
Content (Syllabus outline)

Fundamental elements of kinematics. Description of point mass general motion in Cartesian, polar, cylindrical and natural coordinate system. Differential geometry of space curves from the perspective of kinematics of motion, flexural and torsion curvature. Particular cases of particle motion: linear motion, harmonic motion, circular motion.
Rigid body, degrees of freedom, infinitesimal and finite rotations. General motion of rigid body. Plane motion of rigid body, instant centre of rotation. Motion within rotating frames, absolute and relative coordinate system, Coriolis acceleration and noninertial forces.
Point mass dynamics. Newtonian mechanics. Principle of linear and angular momentum, Newton’s laws, work, energy, power. Potential function.
Dynamics of a system of point masses, centre of mass.
Dynamics of rigid body. Moment of inertia. Transformations of inertia tensor. Dynamics of general motion of rigid body. Rigid body rotation about a fixed axis.

Readings

M. Muršič: Osnove tehniške mehanike 2: Kinematika, DMFA, Ljubljana, 1986.
M. Muršič: Osnove tehniške mehanike 3: Dinamika, Akademska založba, Ljubljana, 1991.
M. Lunn: A first Course in Mechanics, Oxford University Press, 2006.
H. Knudsen: Elements of Newtonian Mechanics, Springer-Verlag, Berlin Heidelberg, 1995.

Objectives and competences

Students will acquire fundamental knowledge and general overview about ingredients of classical mechanics with emphasis on strict mathematical formulation based on previously mastered mathematical knowledge.

Intended learning outcomes

Knowledge and understanding: To establish knowledge and understanding of fundamental principles of classical analytical mechanics.
Application: Mastered coursework represents a foundation for specialized research in the field of mechanics and related areas of natural sciences and technology.
Reflection: Connecting acquired mathematical knowledge within the course with application of that knowledge in a general field of mechanics.
Transferable skills: An overview of classical mechanics within the realm of mathematical apparatus mastered by student during this and other related courses. Solving problems from related areas of applied mathematics.

Learning and teaching methods

Lectures, exercises, homeworks, consultations

Assessment

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

KOC, Pino. Sea-wave dynamic loading of sailing yacht`s retractable keel. Strojniški vestnik, ISSN 0039-2480, Mar. 2014, vol. 60, no. 3, str. 203-209, ilustr. [COBISS-SI-ID 13401627]
KOC, Pino, HALILOVIČ, Miroslav, ŠTOK, Boris. Impact of restrained thermal expansion on NPP Krško primary loop piping. Tehnički vjesnik, ISSN 1330-3651, 2013, god. 20, br. 5, str. 897-904, ilustr. [COBISS-SI-ID 13212955]
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]