Theoretical Physics 1
Code  Completion  Credits  Range 

XP02TF1  Z,ZK  4  3P+1C 
 Course guarantor:
 Petr Kulhánek
 Lecturer:
 Antonín Krpenský, Petr Kulhánek
 Tutor:
 Antonín Krpenský, Petr Kulhánek
 Supervisor:
 Department of Physics
 Synopsis:

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.
 Requirements:

none, first lecture of fourpart cyclus
 Syllabus of lectures:

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.
 Syllabus of tutorials:

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
 Study Objective:

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

[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
 Note:
 Further information:
 www.aldebaran.cz/studium/tf/
 Timetable for winter semester 2024/2025:

06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Wed Thu Fri  Timetable for summer semester 2024/2025:
 Timetable is not available yet
 The course is a part of the following study plans:

 Doctoral studies, daily studies (compulsory elective course)
 Doctoral studies, combined studies (compulsory elective course)
 Doctoral studies, structured daily studies (compulsory elective course)
 Doctoral studies, structured combined studies (compulsory elective course)