Course detail

# Dynamics

The course “Dynamics” makes the students acquaint with basic axioms, laws and principles of theoretical and applied mechanics. Gradually students go over the following areas of dynamics: basic axioms, general dynamics of a particle, dynamics of a system of particles, dynamics of rigid bodies, moments and products of inertia of rigid bodies, dynamics of a system of rigid bodies (planar models), fundamentals of analytical dynamics (Lagrange’s Equations), linear vibration of systems (free, damped and forced vibrations with one degrees of freedom).

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Learning outcomes of the course unit

Dynamics deals with the relationship between motions and forces. Students will be able to analyze motion equations of a particle, body and multi-body systems. Students will solve problems of systems of rigid bodies using dynamic laws and Lagrange's equations. Students will solve a simple linear oscillation system.

Prerequisites

Solving linear equations. Trigonometry and analytic geometry. Differentiation and integration of one variable. Vector algebra. Vector representation of forces and moments. Free body diagrams. Solving homogeneous and general the 2nd order linear differential equations.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

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

The course-unit credit is granted under the condition of active participation in seminars and passing the seminar tests of basic knowledge (at least 10 ECTS points out of 20 must be gained). The points gained in seminar tests are included in the final course evaluation.

Final examination: Written part of the examination plays a decisive role, where the maximum of 80 ECTS points can be reached. The first part of the examination is theoretical test which covers the topic discussed during whole seminars and lectures (maximum 40 ECTS points can be achieved). The second part is numeric solution of two practical problems form dynamics (maximum 40 ECTS points can be achieved).

Solution of several computational problems is demanded. The problems come from typical profile areas of given subject and supplied by a theoretical question, proof, etc. The lecturer will specify exact demands like the number and types problems during the semester preceding the examination.
Final evaluation of the course is obtained as the sum of ECTS points gained in seminars and at the examination. To pass the course, at least 50 points must be reached.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The objective of the course Dynamics is to familiarize students with basic principles of mechanics as well as methods applied for dynamic solving of mechanical systems. The emphasis is on understanding the physical principles governing motion of rigid bodies and applying them to solve simple technical problems in practice.

Specification of controlled education, way of implementation and compensation for absences

Attendance at practical training is obligatory. Head of seminars carry out continuous monitoring of student's presence, their activities and basic knowledge.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Meirovitch, L.: Elements of Vibration Analysis, 2005 (EN)
Slavík J.,Stejskal V.,Zeman V.: Základy dynamiky strojů, 2000 (CS)
Harris V.,M., Crede Ch.: Shock and Vibration Handbook, 2005 (EN)

Recommended literature

Not applicable.

Elearning

Classification of course in study plans

• Programme B-VTE-P Bachelor's 3 year of study, winter semester, compulsory
• Programme B-MET-P Bachelor's 3 year of study, winter semester, compulsory

• Programme B-ZSI-P Bachelor's

specialization STI , 3 year of study, winter semester, compulsory

• Programme LLE Lifelong learning

branch CZV , 1 year of study, winter semester, compulsory

#### Type of course unit

Lecture

26 hod., optionally

Teacher / Lecturer

Syllabus

1. Dynamics of a particle, relative motion of a particle.
2. Dynamics of systems of particles.
3. Rigid body
4. Dynamics of rigid bodies, translational motion, rotation.
5. General plane motion.
6. Three-dimensional motion of a rigid body, gyroscope.
7. Multi-body systems. Application.
8. Rigid bodies dynamics. Methods of solutions.
9. Introduction to analytical dynamics.
10. Single-degree-of-freedom systems.
11. Oscillation of dynamic systems with N DOF.
12. Non-linear oscillation with 1 DOF

Exercise

12 hod., compulsory

Teacher / Lecturer

Syllabus

1. Motion equations of a particle.
2. Motion equations of a particle system.
3. Dynamics of planar and spherical motion.
4. Effects of rotation of rigid bodies on the bearings.
5. Lagrange’s equation of motion.
6. Excited oscillation of system with one degree of freedom.

Computer-assisted exercise

14 hod., compulsory

Teacher / Lecturer

Syllabus

1. Motion equations of a particle.
2. Dynamic systems of particles.
3. Moments and products of inertia.
4. Translational and rotational movement of rigid bodies.
5. General plane motion of rigid bodies.
6. Free oscillation of a system with one degree of freedom.
7. Resonance operation.

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