Know:
• the basic provisions and laws of classical mechanics;
• general theorems and principles of mechanics;
• Modern trends in the development of research in the field of mechanics.
Be able to:
• to study the kinematic and dynamic parameters of structural elements and machines;
• To compile calculation schemes and mathematical models in the theory of linear and nonlinear oscillations and equipment vibration protection;
• carry out analysis of transient and stationary processes of drive mechanisms of machines;
• apply the provisions of theoretical mechanics in scientific research and to solve practical engineering problems.

Pre-requisites: mathematics, physics.

Corrections: resistance of materials, applied mechanics, the theory of mechanisms and machines, parts of machines.

Dynamics. Introduction to Speech. The laws of dynamics. Basic concepts of dynamics. Newton's laws (basic laws of dynamics). Dynamics of free material points. Differential equations of motion of a free material point. Two basic point dynamics tasks. Dynamics of non-free material point. Basic equation of dynamics of non-free material point. Differential equations of motion of non-free material points. Motion of the material point on a smooth surface. Motion of the material point on a smooth surface and line. Movement of the material point on a rough surface. Dynamics of the relative motion of the point. Differential equations of relative motion of a point. Separate cases of relative motion of a point. Relative calm and movement of the body near the Earth's surface. Rectangular vibrations of the material point. Free fluctuations of the material point without taking into account the forces of resistance. Quenching fluctuations of the material point. Aperiodic movement. Forced oscillations of the material point under the action of harmonic disturbing force. Forced oscillations in the absence of resistance. Forced oscillations taking into account the force of linear viscous friction. Forced oscillations of the material point under the influence of arbitrary disturbing force. Introduction to the dynamics of the mechanical system. The division of forces applied to the mechanical system. Differential equations of motion of points of a mechanical system. Geometry of masses System weight. Center of mass Moments of inertia. Axis of inertia. General dynamics theorems. Theorem on the motion of the center of the masses of the mechanical system. Laws of maintaining the movement of the center of the masses of the mechanical system. Number of movement of the material point and the mechanical system. Impulse of force. Theorems on the change in the number of motion of a material point and a mechanical system. Laws of conservation of movement. Theorem on the motion of the center of the masses of a mechanical system .. Theorem on the change of the moment of the amount of motion. Moment of the amount of motion of the material point. Theorem on the change of the moment of the amount of motion of a material point. Kinetic moment of the mechanical system. The kinetic moment of a solid that rotates around a stationary axis. Theorem on the change of the kinetic moment of a mechanical system. The laws of kinetic moment conservation. Theorem on the change of kinetic energy. Two measures of mechanical motion. The kinetic energy of the material point and the mechanical system. Kionig's theorem. Kinetic energy of a solid. Work of forces. The work of force applied to the material point. The work of forces applied to the mechanical system. Work of forces applied to a solid body. Theorems on the change of the kinetic energy of the material point and the mechanical system. Potential power field. Power function. Surface level Power lines. Potential energy. Power function and potential energy of a mechanical system. Examples of potential strength fields. Principles of mechanics. Dalmber's principle for the material point and the mechanical system. The main vector and the main moment of the forces of inertia of the solid. Dynamic solid-state reactions in a rotational motion around a stationary axis. Static and dynamic equilibrium. The subject of analytical mechanics. Classification of ligaments. Possible moves. Possible work of forces applied to the mechanical system. Ideal links The principle of possible moves. General equation of dynamics. Equation of the Lagrange of the second kind. General coordinates of the system. Generalized forces. General equation of dynamics in generalized forces. Condition of equilibrium of forces. The derivation of the Lagrange equations of the second kind. The second-order Lagrange equation for conservative systems.

1. Kuzio IV, Smereka I.P., Van'kovich T.-N.M., Zinko J.A. Theoretical mechanics. Point dynamics. Lviv. View of NU "LP" 2002, 156 p.
2. I.V.Kuzio, I.P. Smereka, T.-N.M. Van'kovich, Ya.A. Zin'ko. Theoretical mechanics. The basic theorems of dynamics. //Tutorial. Lviv, NU "LP", 2005, - 188 p.
3. Pavlovsky MA Theoretical mechanics. Kyiv, 2002
4. IV Kuzio, T.-N.M.Vankovich, Ya.A. Zin'ko, MV Bogenko Theoretical mechanics. Solid state dynamics. Principles of mechanics: Textbook. - Lviv: // Publishing house of the National University "Lviv Polytechnic". 2009. - 132 p.
5. Kuzio IV, Van'kovich T.-N.M., Zin'ko J.A. Theoretical mechanics. Special sections. View at NU "LP", 2011, 156 pp.
6. Kuzio IV, Van'kovich T.-N.M., Zinko YA.A Theoretical mechanics. Dynamics. Kn..1: Teaching. - Lviv: Publishing house "Raster-7", 2012. - 444 p.
7. Kuzio IV, Van'kovich T.-N.M., Zinko YA.A Theoretical mechanics. Dynamics. Book 2: Teaching. - Lviv: Publishing house "Raster-7", 2012. - 338 p.
8. Vekerik VI, Kuzio IV, Tsidilo IV, Liskanich MV The theoretical mechanics album. Ч.ІІ Dynamics. Iv.Frankovsk «View Symphony Forte. 2010, 88 p.
9. Bilyosevich RM, Kuzio IV, Zinko Ya.A., Kos'tov M.I., Mikitin M.Y., Tsikailo T.-N.M. Theoretical mechanics. Workshop on theoretical mechanics for students of technical universities. // Kyiv, IZMN, 1997, 384 p.
10. Smereka I.P., Barvinsky A.F., Belous B.D., Kuzio IV, Zinko J.A. Textbook "A Short Guide to Theoretical Mechanics". // Lviv, View of "Intellect-West", 2001, 240 p.
11. Vekerik VI, Kuzio IV, .Ryzhenko LM, Liskanich MV, Levchuk K.G., Tsidilo IV, Gridzhuk Ya.S. Test tasks and short tasks with theoretical mechanics. Dynamics. // Manual Ivano-Frankivsk: Torch. 2008. 438 p.
12. Vekerik VI, Kuzio IV, Smereka IP, Liskanich MV, Tsidilo IV, Dragan MS Collection of Olympiad Problems in Theoretical Mechanics. //Iv.Frankivsk, View "Fakel", 2003, 139 p.
13. I.V.Kuzio, MVBozhenko, Ya.A. Zin'ko, L.V.Dzyubik Dynamics Laboratory Practicum on Theoretical Mechanics. Part III - Lviv: Publishing house of the National University "Lviv Polytechnic", 2009 -124 p.
14. Bozhidarnik V.V., Velichko L.D. The method of solving and a collection of problems in theoretical mechanics. Lutsk. 2003. 496 с.
15. Apostolyuk OS, Vorobyov V.M., Ilchyshina D.I. etc. Theoretical mechanics. Collection of tasks. K.Technika 2007. 400 с.

- written reports on laboratory work, oral questioning. Multiplication and graphic work (30%); - final control (control measure - examination) written-oral form (70%).

As a result of studying the discipline, the specialist should know the laws, theorems and principles of classical mechanics, the method of kinematic analysis of reducers, the simplest mechanisms, modern directions of development of scientific research in the field of nonlinear oscillation theory, equipment vibration protection, and the improvement of the comfort of vehicles.

The trained specialist must be able to apply the provisions of theoretical mechanics in scientific research and to solve practical engineering problems, to conduct analysis of transient and stationary processes of drive mechanisms of machines.

Previous disciplines: mathematics, physics, computer science.

Concomitant and following disciplines: resistance of materials, parts of machines.

Description of the discipline Lecture classes: Section III. Point dynamics and mechanical system. Introduction to Speech. Basic concepts and definitions. Laws of Galileo-Newton. Differential equations of motion of a material point. Two main tasks of the dynamics. Oscillating motion of the material point. Free oscillations of the material point. Differential equations and the law of free oscillations. Quenching fluctuations of the material point. Coefficient and decrement decreasing. Periodic motion of a point. Forced oscillations of the material point under the action of periodic perturbing force. Properties of forced oscillations. Amplitude-frequency characteristic. The phenomena of beating and resonance. Mechanical system. Geometry of masses System weight. Center of the masses of the mechanical system and its coordinates. Classification of forces acting on a mechanical system. General dynamics theorems. Number of movement of the material point and the mechanical system. Impulse of force. Theorem on the change in the number of motion of a point and system. The law of conservation of movement. Theorem on the motion of the center of mass of the system. The law of preservation of movement of the center of masses. The moment of the number of motion of a point relative to the center and the axis. Theorem on the change of the moment of the amount of motion of a material point. The kinetic moment of the mechanical system relative to the center and axis. Theorem on the change of kinetic moment. The law of kinetic moment conservation. Differential equations of rotation of a rigid body around a stationary axis. Theorem on the change of kinetic energy. Elemental work of power. Work force at the final movement. Work of gravity, elasticity. Power. The kinetic energy of the material point and the mechanical system. Calculation of the kinetic energy of a solid in various cases of its motion. Theorem on the change of kinetic energy of a material point and a mechanical system. Power field, potential force field. Potential energy. The law of conservation of mechanical energy. Dalmber's principle. Inertia force. Dalmber's principle for the material point and the mechanical system. The main vector and the main moment of the forces of inertia. The principle of possible moves. Classification of ligaments. Possible moves. The number of degrees of freedom of the system. Ideal links The principle of possible moves. General equation of dynamics. Practical training: Section III. Point dynamics and mechanical system. 1. Differential equations of motion of a point. The first point dynamics task. The second is the point dynamics task. 2. Vibrations of the material point. Free, fading and forced oscillations. 3. Theorem on the change in the amount of motion of a material point and a mechanical system. Theorem on the change of the moment of the amount of motion of the material point and the mechanical system. Theorem on the motion of the center of mass. 4. Theorem on the change of the kinetic energy of the material point and the mechanical system. 5. Dalmber's principle for the material point and the mechanical system. 6. Principle of possible moves.

Література
1. І. В.Кузьо, Т.-Н. М. Ванькович, Я. А. Зінько, М. В. Боженко. Теоретична механіка. Динаміка твердого тіла. Принципи механіки: Навч. посібник/. – Львів: Видавництво Національного університету «Львівська політехніка». 2009. - 132 с.
3. Смерека І. П., Кузьо І. В., Придиба В. Т., Зінько Я. А.Теоретична механіка. Навчальний посібник для студентів дистанційної форми навчання. Львів. 2004.
4. Смерека І.П., Барвінський А.Ф., Білоус Б.Д., Кузьо І.В., Зінько Я.А. Короткий довідник з теоретичної механіки. Навчальний посібник. Львів, 2001.
5. Божидарнік В.В.. Величко Л.Д. Методика розв’язування і збірник задач з теоретичної механіки. Луцьк. 2003.
6. І. В .Кузьо, Т.-Н. М. Ванькович, Я. А. Зінько. Теоретична механіка. Спеціальні розділи: Навч. посібник/. – Львів: Видавництво Національного університету «Львівська політехніка». 2011. - 110 с.
7. І. В. Кузьо, Т.-Н. М. Ванькович, Я. А. Зінько. Теоретична механіка. Динаміка. Кн. 1. Навчальний посібник. – Львів: «Растр-7», 2012. – 442 с.
8. І. В. Кузьо, Т.-Н. М. Ванькович, Я. А. Зінько.Т еоретична механіка. Динаміка. Кн. 2. Навчальний посібник. – Львів: «Растр-7», 2012. – 336 с.
9. Зінько Я. А. , Кузьо І. В. Збірник задач з теоретичної механіки. Ч. 1 . Статика. Львів: Видавництво Національного університету „Львівська політехніка”. 2015. – 85 с.
10. Кузьо І. В., Зінько Я. А., Ванькович Т.-Н. М. та ін. Теоретична механіка. Підручник для студентів Вищих навч. закл. Харків, Фоліо. 2017. 780 с.
11. Зінько Я. А., Кузьо І. В., Дзюбик Л. В. Збірник задач з теоретичної механіки. ч. ІІ. Кінематика: навч. посібник. Львів: Вид-во НУ «Львівська політехніка», 2017. – 92 с.

Reporting form is an exam
Current control: 30 points
Examination Control (written work): 60 points
Oral component: 10 points