|Přednášející||Martin Žáček, Stanislav Pekárek|
|Cvičící||Martin Žáček, Stanislav Pekárek|
Within the framework of this course students gain the knowledge of selected parts of classical physics and dynamics of the physical systems. The introductory part of the course deals with the mass particle kinematics; dynamics, with the system of mass particles and rigid bodies. The students should be able to solve basic problems dealing with the description of mechanical systems. The introduction to the dynamics of the systems will allow to the students deeper understanding as well as analysis of these systems. The attention will be devoted namely to the application of the mathematical apparatus to the solution of real physical problems. Apart of this, the knowledge gained in this course will help to the students in the study of other disciplines, which they will meet during their further studies.
Knowledge of the differential and integral calculus of the function of one and more variables; linear algebra.
1. Units, system of units. Physical fields. Reference frames.
2. Particle kinematics (rectilinear motion, circular motion, motion in three dimensions.
3. Newton?s laws, inertial and non-inertial reference frames. Equations of motion in inertial and non-inertial reference frames.
4. Work, power, conservative fields, kinetic and potential energy. Conservation of mechanical energy law.
5. Newton´s law of universal gravitation, gravitational field of the system of n particles and extended bodies. Gravitational field intensity, potential.
6. Gravitational field outside and inside a spherical mass shell and homogeneous mass sphere.
7. Mechanical oscillating systems. Simple harmonic motion, damped and forced oscillations. Resonance of displacement and velocity.
8. System of n-particles, isolated and non-isolated systems, conservation of linear and angular momentum laws. Conservation of mechanical energy law for the system of n-particles. Center of mass and center of gravity.
9. Rigid bodies, equations of motion, rotation of the rigid body with respect to the fixed axis. Moment of inertia, Steiner?s theorem
10. Classification of dynamical systems (linear, nonlinear, autonomous, nonautonomous, conservative, continuous, discrete, one-dimensional, multidimensional, time-reversal, time-irreversal). Phase portraits, phase trajectory, fixed points, dynamical flow. Stability of linear systems.
11. Topological classification of linear systems (saddle points, stable and unstable spiral, stable and unstable node, center point).
12. Stability of nonlinear systems, Liapunov stability, limit cycles, bifurcation (Hopf, subcritical, supercritical, transcritical etc.), bifurcation diagram, Poincaré sections, attractors.
13. Deterministic chaos, Lorenz equations, strange attractor.
14. One-dimensional maps, Feigebaum numbers, the logistic equation, fractals.
1. Introduction, safety instructions, laboratory rules, list of experiments, theory of errors - measurement of the volume of solids.
2. Uncertainties of measurements.
3. 2nd Newton´s law and collisions.
4. Torsion pendulum, shear modulus and moment of inertia.
5. Measurement of the acceleration due to the gravity with a reversible pendulum and study of the gravitational field.
6. Young?s modulus of elasticity.
7. Forced oscillations - Pohl´s torsion pendulum.
8. Coupled pendulum.
9. Franck-Hertz experiment and measurement of excitation energy of the mercury atom.
11. Statistical distributions in physics. Poisson´s and Gauss´ distribution - demonstration using the radioactive decay.
12. Measurement of the speed of sound using sonar and acoustic Doppler effect. Diffraction of acoustic waves.
14. Grading of laboratory reports. Assessment.
1. Physics I, S. Pekárek, M. Murla, Dept. of Physics FEE CTU, 1992.
2. Physics I - Seminars, M. Murla, S. Pekárek, Vydavatelství ČVUT, 1995.
3. Physics II, S. Pekárek, M. Murla, Vydavatelství ČVUT, 2003.
4. Physics II - Seminars, S. Pekárek, M. Murla, Vydavatelství ČVUT, 1996.
5. Physics I - II, Laboratory manual, S. Pekárek, M. Murla, Vydavatelství ČVUT, 2002.