CTU FEE Moodle
Theoretical Physics 1
B232 - Summer 23/24
This is a grouped Moodle course. It consists of several separate courses that share learning materials, assignments, tests etc. Below you can see information about the individual courses that make up this Moodle course.
Theoretical Physics 1 - B02TF1
Main course
| Credits | 4 |
| Semesters | Winter |
| Completion | Assessment + Examination |
| Language of teaching | undefined |
| Extent of teaching | 3+1s |
Annotation
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
No data.
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.
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 outlines
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
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: 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
[2] E. M. Lifshitz, L. D. Landau: Course of Theoretical Physics: Mechanics, Pergamon Press, 2003
Requirements
none, first lecture of four-part cyclus
Theoretical Physics 1 - XP02TF1
| Credits | 4 |
| Semesters | Winter |
| Completion | Assessment + Examination |
| Language of teaching | undefined |
| Extent of teaching | 3P+1C |
Annotation
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.
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.
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 outlines
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
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
[2] E. M. Lifshitz, L. D. Landau: Course of Theoretical Physics: Mechanics, Pergamon Press, 2003
Requirements
none, first lecture of four-part cyclus