# Subject description - XP02TF1

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XP02TF1 Theoretical Physics 1
Roles:S Extent of teaching:3P+1C
Department:13102 Language of teaching:
Guarantors:Kulhánek P. Completion:Z,ZK
Lecturers:Krpenský A., Kulhánek P. Credits:4
Tutors:Krpenský A., Kulhánek P. Semester:Z

Web page:

www.aldebaran.cz/studium/tf/

Anotation:

The lecture Theoretical Physics 1 is a basis for the following lectures of theoretical physics for the doctoral study. The main aim is theoretical Mechanics - to master the description of motion in curvilinear coordinates.

Study targets:

To became familiar with basics of the theoretical mechanics. This is first step in study of other theoretical disciplines.

Content:

The lecture Theoretical Physics 1 is a basis for the following lectures of theoretical physics for the doctoral study. The main aim is theoretical Mechanics - to master the description of motion in curvilinear coordinates.

Course outlines:

 1 Generalized coordinates and momenta. State of the system, configuration space. 2 Equations of motion: Hamilton's variational principle, Lagrange equations. 3 Conservation laws in nature: generalized momentum, generalized energy, phase space. 4 Hamilton's canonical equations, Hamilton's function. 5 Poisson formulation of the equations of motion. Poisson equations. Lie algebra. 6 Nonlinear dynamical systems: Solutions of the ordinary differentially equations. 7 Bifurcation. Equation stability and phase space portrait. Ljapunov stability. 8 Attractors. Strange attractors. 9 Chaotic sets, deterministic chaos. 10 Numerical methods. 11 Charged particles motion, drift theory, adiabatic invariants. 12 Magnetic mirrors, tokamaks, stelarators. 13 Particle motion in the magnetic dipole, 14 Particle motion in the Earth magnetic field.

Exercises outline:

generalized coordinates Lagrange equations, examples Hamilton equations, examples, Poisson equations, examples, conservation laws, evolution equations stability and instability attractors solutions of various types of equations method of potential difference schemes motion of charged particles

Literature:

 [1] P. Kulhánek: vybrané kapitoly z teoretické fyziky, AGA 2017 [2] E. M. Lifshitz, L. D. Landau: Course of Theoretical Physics: Mechanics, Pergamon Press, 2003

Requirements:

none, first lecture of four-part cyclus

Keywords:

theoretical mechanics, Hamilton and Lagrange formalism, conservation laws, stability, charged particles

Subject is included into these academic programs:

 Program Branch Role Recommended semester DOKP Common courses S – DOKK Common courses S –

 Page updated 15.6.2024 17:51:22, semester: Z/2024-5, Z,L/2023-4, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)