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Theoretical mechanics

OК.18

Обов’язкова дисципліна для ОП

First

2022/2023

3 Semester

3

The student must know: basic concepts and methods of theoretical physics, including Newton’s basic postulates, Hamilton's and D’Alembert’s principles, basic conservation laws, phase plane method, two-body problem, solid inertia tensor, Euler’s kinematic and dynamic equations, Hamilton's equation, Liuville’s theorem, Hamilton – Jacobi equation. The student must be able to: apply the basic concepts and methods of theoretical mechanics to solve physical problems.

Full-time form

For sufficient mastery of the discipline “Theoretical Mechanics” requires knowledge of the following mathematical courses: “Mathematical Analysis,” “General Algebra”, “Differential Equations”.

The discipline “Theoretical Mechanics” consists of five sections. The first section is devoted to the study of the motion of material points using the Lagrange formalism. The second section studies the linear and nonlinear oscillations of systems with one and many degrees of freedom in the presence of friction forces; images of damping processes on the phase plane with “positive” and “negative” friction are studied. The third section is devoted to the integration of dynamic systems with several degrees of freedom. The fourth section studies the motion of an absolutely rigid body. Finally, the fifth chapter is devoted to Hamilton's formalism, which is the most powerful method of studying mechanical systems.

[1] Гаральд Іро. Класична механіка. Львів, 1999. [2] А.Ф. Федорченко. Классическая механика. Киев, “Вища школа”, 1983. [3] Б.О. Іванов, М.В. Максюта. Задачі з класичної механіки для самостійної роботи студентів. К.:Видавничо-поліграфічний центр “Київський університет”, 2004. [4] Б.О. Іванов, М.В. Максюта. Навчальний посібник “Конспект лекцій із теоретичної механіки”. К.:Видавничо-поліграфічний центр “Київський університет”, 2012. http://matphys.rpd.univ.ua/downloads/courses/theormech/IvanovMaksyuta.pdf [5] К.С. Карплюк. Механіка. К.: РВЦ “Київський університет”, 1998. [6] М.В. Максюта. Методична розробка для самостійної роботи студентів “Додатковий матеріал до курсу лекцій з теоретичної механіки”, КНУ РФФ, 2006.

Lectures, practical classes, individual independent work.

In the academic semester there are two written tests on the material of lectures (MT-1, MT-2). Modular test is credited if the student for this module scored at least 5 points. A maximum of 15 points is awarded for each modular test. According to the results of the semester assessment, a student can receive up to 60 points. Conditions for admission to the exam: the student must have passed all the modular tests and score at least 20 points during the semester.

Ukrainian