Dynamics of the pendulum with periodically varying length

Dynamics of the pendulum with periodically varying length

Oscillations of a pendulum with a periodically varying length and a model of swing

Qualitative analysis of a pendulum with a periodically varying length is conducted. It is proved that there are two periodic solutions having a prescribed amplitude A(n and a period 1 which is an even multiple k of the excitation period. Stability analysis is carried out for the principal parametric oscillations (k"2). In this connection it is shown that such a pendulum cannot serve as a mathem...

Dynamics of a trapped 2 D Bose - Einstein condensate with periodically and randomly varying atomic scattering length

In this work we consider the oscillations and associated resonance of a 2D Bose-Einstein condensate under periodic and random modulations of the atomic scattering length. For random oscillations of the trap potential and of the atomic scattering length we are able to calculate the mean growth rate for the width of the condensate. The results obtained from the reduced ODE's for oscillations of t...

Dynamics of a Pendulum of Variable Length and Similar Problems

In this chapter we study three mechanical problems: dynamics of a pendulum of variable length, rotations of a pendulum with elliptically moving pivot and twirling of a hula-hoop presented in three subsequent sections. The dynamics of these mechanical systems is described by similar equations and is studied with the use of common methods. The material of the chapter is based on publications of t...

Periodically varying externally imposed environmental effects on population dynamics.

Effects of externally imposed periodic changes in the environment on population dynamics are studied with the help of a simple model. The environmental changes are represented by the temporal and spatial dependence of the competition terms in a standard equation of evolution. Possible applications of the analysis are on the one hand to bacteria in Petri dishes and on the other to rodents in the...