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Course info
KME / TEM
:
Course description
Department/Unit / Abbreviation
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KME
/
TEM
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Theoretical Mechanics
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
4
Cred.
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Type of completion
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Oral
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Type of completion
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Oral
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Time requirements
|
Lecture
2
[Hours/Week]
Tutorial
2
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
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Yes
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Automatic acceptance of credit before examination
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Yes in the case of a previous evaluation 4 nebo nic.
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Included in study average
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YES
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Language of instruction
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Czech
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Occ/max
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|
|
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Automatic acceptance of credit before examination
|
Yes in the case of a previous evaluation 4 nebo nic.
|
Summer semester
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0 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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3 / -
|
9 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Winter semester
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Semester taught
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Winter semester
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Minimum (B + C) students
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10
|
Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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Czech
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Internship duration
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0
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No. of hours of on-premise lessons |
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Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
Yes
|
Fundamental course |
Yes
|
Fundamental theoretical course |
Yes
|
Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
|
KFY/TME
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Preclusive courses
|
N/A
|
Prerequisite courses
|
N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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N/A
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Histogram of students' grades over the years:
Graphic PNG
,
XLS
|
Course objectives:
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The student will be introduced to
- the description of discrete non-relativistic mechanical systems and their classification
- basic calculus of variations
- differential and integral principles of mechanics
- Lagrangian and Hamiltonian approach to mechanics
- theory of gyroscops
- theory of vibrations and stability
- Galileo and Lorentz transformation
- special theory of relativity and its application in dynamics of mass point
|
Requirements on student
|
Credit requirements
Active participation in lessons of delievered topic.
Exam requirements
Active knowledge of lectures and the capability to apply the acquired knowledge to the solution of concrete problems.
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Content
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1. Force field, force work in force field. Mass point motion in force field.
2. Dynamics of mass points systems, equations of motion, conservation laws, couplings.
3. Differential principles of mechanics, d´Alembert´s, Gauss and Jourdain principles, principle of virtual work, static and dynamic balance of mechanical systems, static stability
4. Integral principles of mechanics, basic calculus of variations, Hamilton principle, Lagrange equations of I. and II. type, Hamilton equations, Lagrange and Hamilton functions
5. Hamilton-Jacobi theory, H.-J. equations
6. Theory of gyroscops
7. Theory of linear discrete and continuum system vibrations, stability and response of parametric systems
8. Vibration of nonlinear systems, approximate methods of response solution, Lyapunov stability criterions, Floquet theory
9. Basics of relativistic mechanics, space, time, mass, Galileo and special Lorentz transformation, relativistic mechanics of mass point
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Activities
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Fields of study
|
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Guarantors and lecturers
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Literature
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Time requirements
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All forms of study
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Activities
|
Time requirements for activity [h]
|
Preparation for an examination (30-60)
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55
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Contact hours
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52
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Total
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107
|
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
to solve problems of
- statics and kinematics of mass point and rigid body
- matrix and vector calculus
and to perform basic operations of mathematical analysis
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Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
- to use basic knowledge from mathematical analysis (differentiation, integration, solution if special diffrential equations
- to use operations of the matrix and vector calculus in the effectively way
- to assemble equations of motion of mass points and bodies in 2D by means of Newton´s mechanics
- to use basic programming methods |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
- to use basic knowledge from mathematical analysis (differentiation, integration, solution if special diffrential equations
- to use operations of the matrix and vector calculus in the effectively way
- to assemble equations of motion of mass points and bodies in 2D by means of Newton´s mechanics
- to use basic programming methods |
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Learning outcomes
|
Knowledge - knowledge resulting from the course: |
- solution of dynamic problems of mass points, bodies and its assebladge
- formulation of discrete system mechanics tasks using basic theorems of Lagrange and Hamilton mechanics
- basic propeties of solutions as system response to deterministic excitation, stability of equilibrium position or periodic motion
- basic methods for assessment of stability and solution existence of mathematical models of dynamic systems |
Skills - skills resulting from the course: |
- solution of dynamic problems of mass points, bodies and its assebladge
- formulation of discrete system mechanics tasks using basic theorems of Lagrange and Hamilton mechanics
- basic propeties of solutions as system response to deterministic excitation, stability of equilibrium position or periodic motion
- basic methods for assessment of stability and solution existence of mathematical models of dynamic systems |
Competences - competences resulting from the course: |
N/A |
Ability of information transfer to experts and laymen about special problems and about own opinion to its solution |
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Assessment methods
|
Knowledge - knowledge achieved by taking this course are verified by the following means: |
Oral exam |
Oral examination |
Skills - skills achieved by taking this course are verified by the following means: |
Oral examination |
Competences - competence achieved by taking this course are verified by the following means: |
Oral examination |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Practicum |
Skills - the following training methods are used to achieve the required skills: |
Lecture |
Lecture
|
Competences - the following training methods are used to achieve the required competences: |
Lecture |
Lecture |
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