Angular velocity of physical pendulum suspended on movable base

The paper considers a generalized model of some mechanisms presented in the form of a physical pendulum suspended on a rotating platform. The angular velocity of the platform is predetermined and constant. There is no friction of a suspension axis. The Hamiltonian of the system is found. The canonical transformation to action-phase variables is determined. It allows obtaining two relations: the pendulum’s angular velocity and the relation of time to the pendulum’s angular displacement. These relations are considered in terms of correlation between the pendulum’s angular velocity and time. The correlation is defined in a parametric form. This function has no analytical representation. It is presented in the form of a relation calculated using the computer. The algorithm of its implementation in MathCAD software allows online monitoring the dynamic changes of the angular velocity, if the characteristics of a pendulum, a suspension, and the angular velocity of a platform rotation are changing as well.

References

[1] Zaslavskiy G.M., Sagdeev R.Z. Vvedenie v nelineynuyu fiziku: ot mayatnika do turbulentnosti i khaosa [Introduction to nonlinear physics: from the pendulum to turbulence and chaos]. Moscow, Nauka Publ., 1988. 368 p.

[2] Butenin N.V., Neymark Yu.I., Fufaev N.L. Vvedenie v teoriyu nelineynykh kolebaniy [Introduction to the theory of nonlinear oscillations]. Moscow, Nauka Publ., 1976. 385 p.

[3] Landau L.D., Lifshits E.M. Teoreticheskaya fizika. T. 1. Mekhanika [Theoretical physics. Vol. 1. Mechanical science]. Moscow, Nauka Publ., 2001. 220 p.

[4] Ol’khovskiy I.I. Kurs teoreticheskoy mekhaniki dlya fizikov [Course of engineering mechanics for physicists]. Moscow, Izd. Mosk. Univer. Publ., 1978. 575 p.