516-0878/01 – Theoretical Mechanics (TM)
Gurantor department | Institute of Physics | Credits | 5 |
Subject guarantor | RNDr. Jaroslav Foukal, Ph.D. | Subject version guarantor | RNDr. Jaroslav Foukal, Ph.D. |
Study level | undergraduate or graduate | Requirement | Compulsory |
Year | 1 | Semester | winter |
| | Study language | Czech |
Year of introduction | 2004/2005 | Year of cancellation | 2012/2013 |
Intended for the faculties | HGF | Intended for study types | Follow-up Master |
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
Other requirements
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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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.