UFPF003 Selected Topics in Physics I

Faculty of Philosophy and Science in Opava
Winter 2015
Extent and Intensity
3/2/0. 8 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Jan Hladík, Ph.D. (lecturer)
prof. Ing. Ivan Hubač, DrSc. (lecturer)
RNDr. Jan Hladík, Ph.D. (seminar tutor)
prof. Ing. Ivan Hubač, DrSc. (seminar tutor)
Guaranteed by
prof. Ing. Ivan Hubač, DrSc.
Centrum interdisciplinárních studií – Faculty of Philosophy and Science in Opava
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This one-semester course introduces selected topics of Newtonian mechanics of point particles and rigid bodies. Important applications and examples completing the theoretical treatment are illustrated using symbolic and numerical demonstrations in Mathematica.
Syllabus
  • Coordinates and their transformation. Scalars, vectors, tensors and operations with them.
    Kinematics. Velocity, acceleration. Examples (curve of pursuit).
    Newtonian mechanics. Coordinate system, time, mass, laws of motion, force. Conservation laws. Examples (ballistic motion, elastic pendulum).
    Fundamentals of celestial mechanics. Kepler's laws, the law of gravity. Motion in the central field. Collisions and scattering. Examples (pericentre precession in the presence of quadrupole term).
    Calculus Variations. Motivational examples, Euler-Lagrange equations, Euler operator, variations with bonds. Examples (the shortest connection of points, brachistochrone, rotary surface of minimum area, the catenary).
    Lagrangian dynamics. Hamilton's principle, Lagrange function, symmetries and conservation laws. Examples (symbolic derivation of motion the Lagrangian equations using the EulerLagrange operator in Mathematica).
    Hamiltonian dynamics. Legendre transformation, Hamilton canonical equations, Liouville theorem, Poisson brackets, canonical transformations, Hamilton-Jacobi theory, separation of variables. Examples (non-linear oscillator, numerical solutions of equations of motion).
    Chaotic systems, Lyapunov exponents. Examples (magnetic pendulum, logistic map).
    Rigid body. Angular velocity, angular momentum, tensor of inertia, Euler equations. Force-free symmetric top, heavy symmetric top. Examples (spin stabilized magnetic levitation).
    Nonlinear dynamics. Korteweg-de Vries equation, conservation laws. Examples (numerical solution to the KdV equation).
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
Meeting the criteria for obtaining credit in the tutorials. Requirements for successful completion of the examination shall be communicated by the lecturer at the beginning of the semester.
The course is also listed under the following terms Winter 2013, Winter 2014, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020, Winter 2021, Winter 2022.
  • Enrolment Statistics (Winter 2015, recent)
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