Dynamics (FSI-5DT)

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.
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.

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.

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).

Conditions for Granting Course Credit:
Active participation in seminars and obtaining a minimum of 10 points in three ongoing knowledge assessment tests are required. Points from these tests (max. 20 points) contribute to the final course evaluation.

Examination:
The examination is divided into two parts. The first part consists of a comprehensive written test, with a maximum score of 40 points. Progressing to the second part of the examination requires at least 20 points in the first test; otherwise, the examination is graded F. The second part involves written and numerical solutions to typical problems from key areas of the subject, with a maximum score of 40 points. This section consists of two problems covering selected topics discussed during the semester, each graded with 20 points.

The specific format of the examination, types of problems or questions, and grading details will be provided by the lecturer throughout the semester. The final grade is determined by the total points earned from seminars and the examination. To successfully complete the course, a minimum of 50 points is required.

Attendance at seminars is mandatory. Seminar leaders conduct ongoing checks of student attendance, participation, and basic knowledge. Unexcused absences may result in a failure to grant course credit.

Dynamics of a mass point and system of mass points

Mass body(ies) geometry and dynamics of mass body

Dynamics of system of mass bodies, multi-body systems applications

Introduction to analytical mechanics

Single degree of freedom system oscilations

Oscillation of dynamic systems with N DOF

Motion equations of a mass point

Motion equations of a system of maspoints

Dynamics of system of mass bodies

Methods of solving a movement of system of mass bodies (Newton's method, Lagrange’s equation of motion, etc.)

Excited oscillation of system with one degree of freedom

Motion equations of a mass point

Motion equations of a system of maspoints

Dynamics of system of mass bodies

Methods of solving a movement of system of mass bodies (Newton's method, Lagrange’s equation of motion, etc.)

Excited oscillation of system with one degree of freedom

Brousil J.,Slavík J.,Zeman V. : Dynamika, 2002

Slavík J.,Kratochvíl C.: Dynamika, 2005