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Vol 72, No 1 (2017)
- Year: 2017
- Articles: 5
- URL: https://journals.rcsi.science/0027-1330/issue/view/10007
Article
1-6
A form of the solution to the Mathieu equation
Abstract
A special linear transformation is introduced to express the general solution to a second-order differential equation with a periodic coefficient in terms of a particular solution to an auxiliary second-order nonlinear system with a periodically perturbed right-hand side. It is numerically shown that there exist periodic solutions to the auxiliary system outside the instability regions of the solutions to the Mathieu equation. The estimates obtained for the instability regions are in agreement with known results.
7-12
Stability of a falling conducting liquid film in an alternating electric field
Abstract
The flow of a thin viscous conducting liquid film falling along one of the plates of a vertically positioned plane capacitor is studied. The capacitor is connected to an alternating current power supply. It is shown that the presence of the electric field leads to flow destabilization; moreover, the parametric resonance of capillary waves is observed.
13-18
19-22
Effect of the atmospheric electric field under a thundercloud on tornado funnel formation
Abstract
The effect of the atmospheric electric field under a thundercloud on the formation and motion of a tornado funnel is considered. It is shown that the electric force may cause the descent of the developing funnel to the Earth’s surface or its ascent back to the thundercloud.
23-27