Stability of Motion of a System

Training students to independently research in the field of stability of motion of holonomic and nonholonomic mechanical systems, particularly in the case of the stability of the equilibrium position of the stationary motion of mechanical systems, as models of real technical objects.

After this course, students will be able to independently solve problems of stability of mechanical systems.

Nondisturbed and disturbed motion. Stability of a motion. Differential equations of a disturbed motion. Direct Lyapunov’s method. Lyapunov functions. Lyapunov’s theorem of a stability. Lyapunov’s theorem of a asymptotic stability. Lyapunov’s theorem of a instability. Chetayev’s theorem. Lyapunov function and first integrals. Stability in relation to a part of variables. Stability in linear approximation. Stability of equilibrium state and stationary motion. Stability of equilibrium state of conservative systems. Influence of gyroscopic and dissipative forces. Stability of equilibrium state and stationary motion of a nonholonomic systems.

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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: 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

Malkin I., Theory of Stability of a Motion, (in Russian), Nauka, Moscow, 1966.; Bakša А.,Vesković M., Stability of a motion (in Serbian), Faculty of Mathematics, Belgrade, 1996.