Rotated pendulum

- Derivation of mathematical models of a classical pendulum without damping and forcing and

of a pendulum with damping.

- Construction of a mathematical model of a rotated pendulum.

- The models will be in the form of a differential system with parameters, which can be investigated by methods of the theory of dynamical systems.

- Description of the methods and their application to the model of the rotated pendulum.

- Determination of critical points and phase portraits.

- Investigation of a dependence of the phase portraits on changes of parameters contained in the model.

- Creation of phase portraits for given values of parameters by a mathematical software.

Literature:

J.K.Hale, H. Kocak : Dynamics and Bifurcations, Springer, New York 1991.

L. Perko: Differential Equations and Dynamical Systems, Springer, New York 1993.

J.H. Hubbard, B.H. West: Differential Equations : A Dynamical Systems Approach, Springer, New York 1995.

J.Kalas, M. Ráb : Obyčejné diferenciální rovnice, MU Brno, 199.