A note on bifurcation of equilibrium forms of a gas baloon parachute

Anita Zgorzelska; Hanna Guze

Published: 2025-05-20

2024

A note on bifurcation of equilibrium forms of a gas baloon parachute

Anita Zgorzelska

, Hanna Guze

Abstract

We will be concerned with deformations of a free elastic top rim of a parachute of a gas balloon. The top rim is connected with the circular deflation port of the balloon envelope by heavy duty flexible load tapes. The inside part of the balloon is filled with compressed gas. Equilibrium forms of the parachute may be found as solutions of a certain nonlinear functional-differential equation with two physical parameters: an elasticity coefficient of tapes and a physical parameter describing compressed gas. This equation possesses radially symmetric solutions corresponding to circular shapes of the top rim. Our goal is to study the existence of symmetry breaking bifurcation of the top rim of parachute.

Keywords:

free boundary problem , Fredholm map , gas balloon , subcritical bifurcation , symmetry-breaking bifurcation

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Zgorzelska, A., & Guze, H. (2025). A note on bifurcation of equilibrium forms of a gas baloon parachute. Annales Mathematicae Silesianae. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/19073

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2024
Published: 2024-01-18

ISSN: 0860-2107

eISSN: 2391-4238

10.2478/amsil

Publisher

University of Silesia Press

Licence CC

This work is licensed under a Creative Commons Attribution 4.0 International License.

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