Stability and instability of small motions of a pendulum with a cavity filled with a system of ideal capillary fluids

Authors

  • Wadia Ali

Abstract

الهدف من هذا البحث هو دراسة المسألة الطيفية للحركات الصغيرة لنواس ذي تجويف مملوء بمجموعة من السوائل الشعرية المثالية عندما يتحقق شرط الاستقرار بالتقريب الخطي. فقد تم البرهان على أن لهذه المسألة طيفاً حقيقياً متقطّعاً له نقطة تراكم عند  وأن القيم الخاصة لهذه المسألة هي نهايات صغرى متتالية لنسب متغيرة، كما تم البرهان على أنه إذا كان لمؤثر الطاقة الكامنة لجملة ( نواس + مجموعة سوائل شعرية مثالية )  قيمة خاصة سالبة فإن حلول المسألة الحدية الابتدائية لهذه الجملة غير مستقرة.

The aim of this paper is to study the spectral problem of small motions of a pendulum with a cavity filled with a system of ideal capillary fluids when the condition of statically stable in linear approximation is valid. It is proved that this problem has a real discrete spectrum with a limit point at and the eigenvalues for this problem are successive minima of variation ratio. It is also proved that if the operator of potential energy of a system ( pendulum + a system of ideal capillary fluids )has a negative eigenvalues, then the solutions of the initial boundary value problem are instable.

 

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Published

2019-08-19

How to Cite

1.
Ali W. Stability and instability of small motions of a pendulum with a cavity filled with a system of ideal capillary fluids. TUJ-BA [Internet]. 2019Aug.19 [cited 2024Apr.18];36(4). Available from: https://journal.tishreen.edu.sy/index.php/bassnc/article/view/1027

Issue

Vol. 36 No. 4 (2014): العلوم الأساسية

Section

Articles

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