516-0878/01 – Theoretical Mechanics (TM)

Gurantor departmentInstitute of PhysicsCredits5
Subject guarantorRNDr. Jaroslav Foukal, Ph.D.Subject version guarantorRNDr. Jaroslav Foukal, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction2004/2005Year of cancellation2012/2013
Intended for the facultiesHGFIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
FOU20 RNDr. Jaroslav Foukal, Ph.D.
MAD20 prof. RNDr. Vilém Mádr, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 12+0

Subject aims expressed by acquired skills and competences

Analyse some kinematic and dynamic problems solution of Newtonian mechanics Formulate the basic differential and integral principles of theoretical mechanics Interpret the theoretical mechanics equations Evaluate connection between theoretical and quantum mechanics

Teaching methods

Lectures
Tutorials

Summary

Obsahem předmětu Teoretická mechanika je přehledné shrnutí a zobecnění kinematického a dynamického popisu pohybu částice, soustavy částic a tuhého tělesa. K popisu pohybu se využívá skalární analytické mechaniky (Lagrangeovy a Hamiltonovy), která vychází z několika obecných diferenciálních a integrálních principů.

Compulsory literature:

1. Brdička, M., Hladík, A.: Teoretická mechanika, Academia, Praha 1987 2. Obetková, V., Mamrillová, A., Košinárová, A.: Teoretická mechanika, Alfa, Bratislava 1990 3. Leech, J. W.: Klasická mechanika, SNTL, Praha 1970 4. Landau, L. D., Lifšic, E. M.: Mechanika, Nauka, Moskva 1965 5. Kvasnica, J. a kol.: Mechanika, Academia, Praha 1988

Recommended literature:

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

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Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1st Kinematics and dynamics of particles Classical particle (material point). Generalized coordinates, orthogonal coordinate systems, generalized velocity, generalized acceleration. Axioms of classical mechanics, Newton's laws of motion. Generalized power. Solving Newton's equations of motion. Momentum, angular momentum, conservation laws. The kinetic and potential energy of particles. Potential, gyroscopic and dissipative forces. 2nd The system of particles withouth constraints D'Alembert´s principle. Solid particle system. The first integrals of motion for systems of particles. Momentum, angular momentum for a system of particles. The center of gravity. Impulse-momentum theorems and their consequences. König´s theorem. The total mechanical energy of a system of particles. 3rd Systems of particles undergoing constreints Constraint, equation of constraint, classification of constraints. A virtual displacement, virtual displacement conditions. The principle of virtual work. D'Alembert – Lagrange´s principle. Force of constraint. Lagrange´s equations of the 1st type. Degrees of freedom of mechanical system. Lagrange´s equations of the 2nd type. Lagrangian function. Another differential principles of mechanics. Some methods of solving Lagrange´s equations of the 2nd type (integral cyclic coordinates, the integral energy). Rayleigh´s dissipative function. Hamilton's canonical equations. Hamiltonian function. Solving Hamilton's equations (cyclic coordinates, the integral energy). Legendreś transformation. Routh´s equations. 4th General principles of mechanics Calculus variations (variation function, the fundamental role of the calculus of variations). Configuration space, configuration trajectory. Phase space, phase trajectory. Hamilton's principle, action integral. Hamilton's principle of equivalence and the principle of virtual work. Principle of minimal action, short action (Hamilton's characteristic function). Maupertuis´s principle, Jacobi's principle, Fermat's principle. 5th Canonical transformation Transformation of coordinates in phase space that preserves the shape of the canonical equations. Generating function of canonical transformation. Examples of canonical transformations. Hamilton – Jacobi´s method. Poisson´s brackets, the rules for working with Poissonś brackets. Poisson brackets and integrals of motion. Poisson's theorem on the relations between the integrals of motion.

Conditions for subject completion

Full-time form (validity from: 2012/2013 Winter semester, validity until: 2014/2015 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 30 (30) 15
                Written exam Written test 30  15
        Examination Examination 70 (70) 35
                Written examination Written examination 30  15
                Oral Oral examination 40  20
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2012/2013 (N2102) Mineral Raw Materials (3911T001) Applied Physics of Materials P Czech Ostrava 1 Compulsory study plan
2011/2012 (N2102) Mineral Raw Materials (3911T001) Applied Physics of Materials P Czech Ostrava 1 Compulsory study plan
2010/2011 (N2102) Mineral Raw Materials (3911T001) Applied Physics of Materials P Czech Ostrava 1 Compulsory study plan
2009/2010 (N2102) Mineral Raw Materials (3911T001) Applied Physics of Materials P Czech Ostrava 1 Compulsory study plan
2008/2009 (N2102) Mineral Raw Materials (3911T001) Applied Physics of Materials P Czech Ostrava 1 Compulsory study plan
2007/2008 (N2102) Mineral Raw Materials (3911T001) Applied Physics of Materials P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner