Theoretical Mechanics (FSI-STM-A)

Academic year 2020/2021

Supervisor:	prof. RNDr. Michal Kotoul, DrSc.
Supervising institute:	ÚMTMB	all courses guaranted by this institute
Teaching language:	English
Aims of the course unit:
The aim of the course “Theoretical Mechanics” is to make students familiar with basic axioms, laws and principles of classical mechanics.
Learning outcomes and competences:
Students will master basic methodological and logical approaches to the dynamic solution of mechanical systems. The matrix notation is used and therefore the students will be able to solve dynamic problems using computers.
Prerequisites:
In the field of mechanics: Vectorial representation of forces and moments. Free body diagrams. In the field of mathematics: Trigonometry and analytic geometry. Vector algebra. Solution to the system of linear and quadratic equations. Differential and integral calculus of one variable. Solution of ordinary differential equations of 2nd order.
Course contents:
Kinematic relations and quantities (position, velocity, acceleration) related to the motion of a point, a rigid body and an assembly of rigid bodies are discussed. Also dealt with is the kinematic solution of rectilinear motion, rotary motion, spherical motion and general motion. In the case of relative motion the corresponding kinematic quantities are given. Subsequently, basic terms of dynamics of a particle, mass-geometric characteristics of rigid bodies, dynamics of rigid body/assembly of rigid bodies are presented in terms of vectorial dynamics. The foundations of analytical dynamics are then explained. In the end the theory of vibration of mechanical systems with n degrees of freedom together with the foundations of gyratory vibration of shafts are delivered.
Teaching methods and criteria:
The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.
Assesment methods and criteria linked to learning outcomes:
Written test examining the knowledge of basic concepts - examination paper containing 3 examples to be solved - oral discussion over examination papers with an optional additional question.
Controlled participation in lessons:
Attendance is required. One absence can be compensated by attending a seminar with another group in the same week, or by elaboration of substitute tasks. Longer absence is compensated by special tasks according to instructions of the tutor. Course-unit credit is awarded on the following conditions: - active participation in the seminars, - good results in seminar tests of basic knowledge, - solution of additional tasks in case of longer excusable absence. Seminar tutor will specify the form of these conditions in the first week of semester.
Type of course unit:
Lecture	13 × 3 hrs.	optionally
Exercise	13 × 2 hrs.	compulsory
Course curriculum:
Lecture	Kinematics of a particle. Kinematics of a rigid body. Special cases of rigid body motion: rotation about fixed axis, absolute general plane motion. Special cases of rigid body motion in 3D:translation, spherical motion, general motion. Analysis of relative motion, simultaneous rotations. Dynamics of a particle, inertial and non-inertial reference systems. Equations of motion for a system of particles. Moments of inertia, deviation moments. Dynamics of general motion of rigid body. Dynamic solution to special cases of rigid body motion: translation, rotation, general plane, spherical and screwed motion respectively. Dynamics of rigid body system. Introduction to analytical mechanics. General equation of dynamics. Hamilton principle. Solution of stability problems. Fundamentals of linear theory of vibration with 1 and n degree of freedom. Various kinds of damping. Forced vibration. Gyratory vibration of rotors with 1 and n degree of freedom. Introduction to the nonlinear theory of vibration.

Exercise	Kinematics of rectilinear and curvilinear motion of a particle. Orthogonal transformations. Translation, rotation about fixed axis and absolute general plane motion respectively of a rigid body. Spherical motion and screwed motion of a rigid body. Compound motion, simultaneous rotations, kinematics of transmissions. Solution to the problems of particle dynamics. Dynamics of a system of particles. Dynamics of translation and rotation of a rigid body. Dynamics of general plane motion and spherical motion of a rigid body. Lagrangian equations. Vibration of a system with 1 and n degrees of freedom., free vibration, damped vibration. Forced vibration of a system with 1 and n degrees of freedom. Gyratory vibration of shafts. Examples of nonlinear vibration solution.

Literature - fundamental:
1. Meriam J.L.: Engineering Mechanics, , 0
2. Meirovitch L.: Elements of Vibration Analysis, , 0
3. Slavík J., Stejskal V., Zeman V.: Základy dynamiky strojů, , 0
Literature - recommended:
1. Přikryl K.: Kinematika, , 0
2. Slavík J., Kratochvíl C.: Dynamika, , 0
3. Brousil J., Slavík J.: Dynamika, , 0