-to provide students knowledge of the fundamental principles and methods in Analytical Mechanics -to enable students to solve practical problems in Analytical Mechanics using acquired knowledge in Analytical Mechanics -to prepare students to monitoring novelties in science and engineering

-to enable students to master terms, methods and principles in Analytical Mechanics -to enable students to relate the knowledge from Analytical Mechanics with knowledge in other scientific fields, to apply knowledge from Analytical Mechanics in analysis, synthesis and prediction of solutions and consequences of problems in science

Free and constrained mechanical system. Contraints and their classification. Introductory treatise of generalized coordinates. Quasi-velocities and quasi-coordinates. Possible and virtual displacements. Ideally smooth constraints. Differential principles of mechanics and their application in differential equations forming. Lagrange’s equations of first and second kind. Energy integral. Cyclic coordinates and cyclic integral. Routh’s equations. Function of acceleration and Appell’s equations. Integral principles. First and second form of Hamilton’s principle. Canonical equations. Lagrange’s principle of steady action. Geometrical interpretation of particle’s and mechanical system’s motion. Hertz’s principle of the least curvature.

Free and constrained mechanical system. Contraints and their classification. Introductory treatise of generalized coordinates. Quasi-velocities and quasi-coordinates. Possible and virtual displacements. Ideally smooth constraints. Differential principles of mechanics and their application in differential equations forming. Lagrange’s equations of first and second kind. Energy integral. Cyclic coordinates and cyclic integral. Routh’s equations. Function of acceleration and Appell’s equations. Integral principles. First and second form of Hamilton’s principle. Canonical equations. Lagrange’s principle of steady action. Geometrical interpretation of particle’s and mechanical system’s motion. Hertz’s principle of the least curvature.

Defined by the curriculum of PhD studies program

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: 5
Review and grading of the project: 0
Test: 0
Test: 0
Final exam: 10

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

Anđelić T., Stojanović R., Rational Mechanics, Institute for the publication of textbooks SRS, Belgrade, 1966.; Lurie A.; Analytical Mechanics, State Publishing House of Physical and Mathematical Literature, Moscow, 1966.; Ganthmacher F.; Analytical Mechanics, Institute for the publication of textbooks SRS, Belgrade, 1963.; Radovanović V.; Theoretical mechanics, Lagrangian and Hamiltonian mechanics, Faculty of Physics, University of Belgrade