Theoretical Physics 1

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 four-part 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/

Time-table 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	roomT2:C3-337 Kulhánek P. Krpenský A. 09:15–11:45 (lecture parallel1) Dejvice roomT2:C3-337 Kulhánek P. Krpenský A. 11:45–12:30 (lecture parallel1 parallel nr.101) Dejvice
Fri

Time-table for summer semester 2024/2025:

Time-table 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)