Počet kreditů 4
Vyučováno v Winter
Rozsah výuky 3+1s
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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.

none, first lecture of four-part cyclus

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.

generalized coordinates

Lagrange equations, examples

Hamilton equations, examples,

Poisson equations, examples,

conservation laws,

evolution equations

stability and instability


solutions of various types of equations

method of potential

difference schemes

motion of charged particles

[1] P. Kulhánek: Teoretická mechanika, ČVUT, 2001. http://www.aldebaran.cz/studium/mechanika.pdf

[2] E. M. Lifshitz, L. D. Landau: Course of Theoretical Physics: Mechanics, Pergamon Press, 2003

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