Dance theory and analytical mechanicsSyllabus

Subject code

MİFS-2981

Credits

6

Student workload

180

Semester

Autumn semester

Academic year

2025-2026

Subject type

Elective

Form of education

Full-time

Language of instruction

Azerbaijani

In-class hours

a)30 saat- mühazirə, b)15 saat-seminar

Out-of-class hours

a)90 saat-TSİ, b) 45 saat-MRTSİ

"dance theory and analytical mechanics" subject 060630 is one of the fundamental specialty subjects, designed for graduate students studying mechanical engineering at the master's level and covering advanced dynamic analysis of mechanical systems. the main goal of teaching the subject is to teach undergraduates how to construct the equations of motion of complex mechanical, machine and robot systems by analytical methods and the mathematical analysis of the dance processes occurring in these systems. the variational principles of analytical mechanics, lagrangian, hamiltonian and canonical equations, as well as the theory of free, forced and parametric oscillations of linear and nonlinear systems are deeply explored in the course. at the same time, important research and practical engineering problems such as stability of systems, resonance phenomena and damping of oscillations are given ample space. this subject forms the academic competencies necessary for undergraduates to predict dynamic loadings encountered in the fields of modern mechanical engineering, automation, and device manufacturing, to model dynamic systems, and to conduct independent scientific and research work.

• lecture
• seminar
• presentations
• teamwork

No learning outcomes have been added.

1. 1.
   An introduction to the theory of dances. mechanical systems and their degrees of freedom. free oscillations of the system. analysis of damped and forced oscillations in mechanical systems. longitudinal, transverse and torsional oscillations in machine shafts.Lecture
2. 2.
   Resonance phenomenon. the number of critical cycles of the shaft. torsional dances of the crankshaft. vibrations and oscillations of reciprocating machines. masses brought in the elbow-slider mechanism.Lecture
3. 3.
   Linear oscillations of mechanical systems with infinite degrees of freedom. differential equations of longitudinal oscillations of machine parts and their solutions. differential equations of transverse and torsional oscillations of machine parts and their solutions.Lecture
4. 4.
   Vibrations and oscillations of reciprocating machines. masses transported in the elbow-slide mechanism. transverse dances of boards. basic simplifications and expressions. boundary conditions.Lecture
5. 5.
   Theory of stability of movement of machines. stability of the equilibrium state of the system. lyapunov's theorem about stability of motion.Lecture
6. 6.
   General methods of nonlinear mechanics. forced oscillations of non-linear systems (b. galerkin's method). mechanical oscillations of systems with a finite number of degrees of freedom.Lecture
7. 7.
   Dances along the stick. transverse dances of the string. oscillatory motion of the flow of an ideal fluid in a pipeline.Lecture
8. 8.
   Introduction to analytical mechanics. stability of the equilibrium state of the system.Lecture
9. 9.
   A system of non-free material points. ideal and real communications.Lecture
10. 10.
    The principle of possible displacements. general equation of dynamics.Lecture
11. 11.
    Differential equations of motion of the system in generalized coordinates.Lecture
12. 12.
    Equilibrium conditions of non-free system. lagrange's equations of the 2nd kind.Lecture
13. 13.
    Study of the mechanical movement of machines by means of lagrange's equations of the 2nd type.Lecture
14. 14.
    Generalized coordinates of the elbow-slider mechanism, application of lagrange's equations of the 2nd type to them.Lecture
15. 15.
    Application of lagrange's equations of the 2nd type to compressors and pumps.Lecture

No reading list has been added.