Mechanics of Nonholonomic Systems

The goal of this course is to introduce students to the concepts, principles and methods in Mechanics of Nonholonomic Systems to enable practical problems using acquired knowledge of Mechanics of Nonholonomic Systems for monitoring and enable innovation in science and profession

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

Basic concepts: analytical definitions of constraints, possible displacements, similarity of variational and differential operations. Differential equations of motion of non-holonomic systems with linear non-holonomic constraints of first order: equations of motion forming by means of Lagrange-D’Alembert’s principle, equations of motion in quasi-coordinates, determination of reactions of constraints. First integrals of equations of motion of non-holonomic systems: linear and quadratic integrals, integral of energy, generalized integrals of energy, cyclic integrals. Variational principles in mechanics of non-holonomic systems: Hamilton-Ostrogradsky’s principle, Gauss’ principle, Hertz’s principle,. Stability of motion of non-holonomic systems: equilibrium, stability of steady motions. Non-holonomic systems having constraints of general kind: equations of motion having constraints of general kind. Technical problems of stability of systems with rolling: theory of motion of elastic pneumatic tire.

Basic concepts: analytical definitions of constraints, possible displacements, similarity of variational and differential operations. Differential equations of motion of non-holonomic systems with linear non-holonomic constraints of first order: equations of motion forming by means of Lagrange-D’Alembert’s principle, equations of motion in quasi-coordinates, determination of reactions of constraints. First integrals of equations of motion of non-holonomic systems: linear and quadratic integrals, integral of energy, generalized integrals of energy, cyclic integrals. Variational principles in mechanics of non-holonomic systems: Hamilton-Ostrogradsky’s principle, Gauss’ principle, Hertz’s principle,. Stability of motion of non-holonomic systems: equilibrium, stability of steady motions. Non-holonomic systems having constraints of general kind: equations of motion having constraints of general kind. Technical problems of stability of systems with rolling: theory of motion of elastic pneumatic tire.

Defined by the curriculum study 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: 2
Review and grading of the project: 0
Test: 0
Test: 0
Final exam: 13

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

Andjelic T., Stojanovic R.; Rational Mechanics, Belgrade, 1965.; Dobronravoff V.; Principles of Mechanics of Non-holonomic Systems, Nauka, Moscow, 1970.; Pars L.; Treatise on Analytical Dynamics, Nauka, Moscow, 1971.