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Lecturer(s)
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Dupal Jan, Prof. Dr. Ing.
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Course 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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Learning activities and teaching methods
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Lecture, Practicum
- Contact hours
- 52 hours per semester
- Preparation for an examination (30-60)
- 55 hours per semester
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| prerequisite |
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| Knowledge |
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| 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 |
| Skills |
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| - 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 |
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| - 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 |
| learning outcomes |
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| Knowledge |
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| - 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 |
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| - 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 |
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| N/A |
| Ability of information transfer to experts and laymen about special problems and about own opinion to its solution |
| teaching methods |
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| Knowledge |
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| Lecture |
| Practicum |
| Skills |
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| Lecture |
| Lecture |
| Competences |
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| Lecture |
| Lecture |
| assessment methods |
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| Knowledge |
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| Oral exam |
| Oral examination |
| Skills |
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| Oral examination |
| Competences |
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| Oral examination |
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Recommended literature
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Brdička, Miroslav; Hladík, Arnošt. Teoretická mechanika : Celost. vysokošk. učebnice pro stud. matematicko-fyz. a pedagog. fakult, stud. oboru učitelství všeobecně vzdělávacích předmětů. 1. vyd. Praha : Academia, 1987.
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Horský, J.-Novotný, J.-Štefaník, M.:. Mechanika ve fyzice. Academia Praha, 2001. ISBN 80-200-0208-1.
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Rosenberg Josef. Teoretická mechanika. Západočeská univerzita v Plzni, 2003. ISBN 80-7082-938-9.
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