516-0923/02 – Theoretical Mechanics (FS)

Gurantor departmentInstitute of PhysicsCredits10
Subject guarantorprof. RNDr. Richard Dvorský, Ph.D.Subject version guarantorprof. RNDr. Richard Dvorský, Ph.D.
Study levelpostgraduateRequirementOptional
YearSemesterwinter + summer
Study languageCzech
Year of introduction2003/2004Year of cancellation2012/2013
Intended for the facultiesHGFIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
DVO54 prof. RNDr. Richard Dvorský, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 20+0
Part-time Examination 20+0

Subject aims expressed by acquired skills and competences

To learn the basic concepts of theoretical mechanics according to the given curriculum. To apply the knowledge acquired to basic examples and special tasks according to instructions of the person guaranteeing the subject. To prepare the application of the mentioned knowledge according to the assignment of topic of PhD thesis.

Teaching methods

Lectures
Individual consultations

Summary

The subject deals with kinematics and dynamics of systems of particles and a solid body, differential mechanical principles, integral mechanical principles, canonical equations and transformations, a solid body. Emphasis is placed on the kinematics of rotational motion of solid body, dynamics of solid body, such as the equivalence of systems of forces acting on a solid body, Euler dynamic equations, the Lagrange function for a moving solid body.

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

Recommended literature:

1. Kvasnica, J. a kol.: Mechanika, Academia, Praha 1988

Way of continuous check of knowledge in the course of semester

E-learning

Other requirements

individual and systematic study

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

0. Basic concepts of kinematics and dynamics of systems of particles and rigid bodies 1.Equations of motion of free particles and system of free particles in general coordinates Lagrange equations of the second kind, a generalization forces, generalized potential Lagrangian, conservative force, dissipative force. 2.Dynamics of bound particles and rigid bodies The principle of relaxation, Lagrangian equations of the first kind, Lagrange equations second kind for holonomic systems. 3.Differential mechanical principles The principle of virtual work, reversible and irreversible shift, the equilibrium conditions coupled mechanical systems. D'Alembert's principle, the inertial force, d'Alembert principle of continuity Lagrange equations of the first kind. Central Lagrange equation and its write using the general momentum associated with Lagrange's equations second kind. Differential variational principles: the principle of Gauss, Jourdainův principle. 4.Integral mechanical principles Hamilton's principle, Lagrange equations for invariance bodobých transformations, first integrals Lagrange equations. Maupertuisův principle Jacobi principle. 5.Canonical equations and transformation Hamilton's equations, Hamilton's functions, Legendre transformation, derivation canonical equations of Hamilton's principle, Poisson brackets. Canonical transformations, invariants of canonical transformations. Hamilton- Jacobi equation. 6.Rigid body Kinematics of rotational motion of a rigid body: folding the final turn, Euler angles, Euler kinematic equations. Dynamics of a rigid body: equivalence system of forces acting on a rigid body, the center of the system parallel forces, translational and rotational motion of a rigid body, tensor inertia of a rigid body, Euler dynamic equations of rigid rotation around a fixed point and a fixed axis, moving Lagrangian rigid body.

Conditions for subject completion

Part-time form (validity from: 2003/2004 Winter semester, validity until: 2012/2013 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2010/2011 (P1701) Physics (1702V001) Applied Physics P Czech Ostrava Optional study plan
2010/2011 (P1701) Physics K Czech Ostrava Optional study plan
2010/2011 (P1701) Physics (1702V001) Applied Physics K Czech Ostrava Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner