The goal of this course is that students learn the basic elements: analytical mechanics, dynamics of rigid bodies system, stability of mechanical systems, oscillation of mechanical systems, optimal control theory.

By gaining knowledge in this course, students will be able to carry out research in the fields of mechanical engineering, where there are problems of mechanics of rigid bodies. Students will be able to solve the basic problems of analytical mechanics, dynamics of rigid bodies system, stability of mechanical systems ...

General principles of mechanics. Lagrange principle. Dalamber-Lagrange principle Lagrange's equations of the second kind (covariant and contravariant form). Analysis of Lagrange's equations. Hamilton's principle. The canonical equations. The dynamics of a system of rigid bodies. The stability condition of the mechanical system. Fundamentals of linear oscillations of mechanical systems. Control. Permissive control. Optimal control. Optimality.

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Defined by the curriculum study of PhD studies program.

Vuković J., Selected chapters of mechanics, Handouts, Faculty of mechanical engineering, Belgrade 2006.

Total assigned hours: 65

New material: 50
Elaboration and examples (recapitulation): 0

Auditory exercises: 0
Laboratory exercises: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 10
Review and grading of the project: 0
Test: 0
Test: 0
Final exam: 5

Activity during lectures: 0
Test/test: 0
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 50
Project: 0
Final exam: 50
Requirement for taking the exam (required number of points): 30

Gantmaher F.R., Analytical mechanics, (in Russian), Zavod za izdavanje udžbenika SRS, Belgrade 1963.; Pontrjagin L.S., Mathematical theory of optimal control, (in Russian), Fizmatgiz, Moscow 1961.; Leitmann G., An Introducyion to Optimal Control, McGraw-Hill Book Company, 1966.; Rao S.S.: Mechanical vibrations, Addison-Wesley Publishing Company Inc., 1995.; Bakša А.,Vesković M., Stability of a motion (in Serbian), Faculty of Mathematics, Belgrade, 1996.