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Finding the equilibrium centers in the gravitational fields of some material curves

إيجاد مراكز التوازن في حقول جاذبية بعض المنحنيات المادية

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 Publication date 2015
and research's language is العربية
 Created by Shamra Editor




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In the paper, we study gravitational field generated by a special type of homogeneous material curves that are denoted circumscribed curves. Characteristic state of these curves is the linking of each one of them to a circle, and the circumscribing of him around the circle, or an arc of him, according to a precise meaning. The circumscribed curve consists of arcs of a circle, and straight segments, their right supports are tangents to the circle. In special case, where this curve is a polygon, the sides are tangents to a circle. In this case, we call the polygon, circumscribed polygon. The study shows that the center of the circle, around it, a homogeneous material curve circumscribed, is an equilibrium center.


Artificial intelligence review:
Research summary
يدرس هذا البحث حقل الجاذبية الذي يولده نوع خاص من المنحنيات المادية المتجانسة، والتي تُدعى بالمنحنيات المحبطة. تتميز هذه المنحنيات بارتباطها بدائرة أو قوس منها، وتتكون من أقواس دائرة وقطع مستقيمة تمس تلك الدائرة. في حالة كون المنحني مضلعاً، تكون أضلاعه محمولة على مماسات لتلك الدائرة، ويُدعى المضلع في هذه الحالة بمضلع محبط. يوضح البحث أن مركز الدائرة التي يحيط بها منحني مادي متجانس هو مركز توازن في حقل جاذبية ذلك المنحني. يتناول البحث أيضاً تعريفات ومفاهيم متعلقة بالمنحنيات ذات المركز المماسي، ويقدم برهاناً على أن مركز الدائرة هو المركز المماسي الوحيد لها. كما يناقش البحث حقل الجاذبية الناتج عن منحنيات مادية محيطة ومتجانسة، ويستنتج أن مركز الدائرة هو مركز توازن لحقل جاذبية أي منحني متجانس يحيط بها.
Critical review
دراسة نقدية: يقدم البحث مساهمة هامة في مجال دراسة حقول الجاذبية الناتجة عن منحنيات مادية متجانسة، ويعتمد على مفاهيم رياضية دقيقة لتعريف وتحليل هذه المنحنيات. ومع ذلك، يمكن توجيه بعض الانتقادات البناءة. أولاً، البحث يركز بشكل كبير على الحالات الخاصة مثل المنحنيات المحبطة والمضلعات المحبطة، وقد يكون من المفيد توسيع الدراسة لتشمل أنواع أخرى من المنحنيات. ثانياً، البرهان الرياضي المستخدم في البحث معقد ويحتاج إلى تبسيط وتوضيح أكثر ليكون مفهوماً بشكل أفضل للقراء غير المتخصصين. أخيراً، البحث لم يتطرق بشكل كافٍ إلى التطبيقات العملية لهذه النتائج، والتي يمكن أن تكون مفيدة في مجالات مثل الفيزياء الفلكية والهندسة.
Questions related to the research
  1. ما هي المنحنيات المحبطة؟

    المنحنيات المحبطة هي منحنيات مادية متجانسة ترتبط بدائرة أو قوس منها، وتتكون من أقواس دائرة وقطع مستقيمة تمس تلك الدائرة.

  2. ما هو مركز التوازن في حقل الجاذبية الناتج عن منحني مادي متجانس؟

    مركز التوازن هو مركز الدائرة التي يحيط بها المنحني المادي المتجانس.

  3. ما هو المركز المماسي للمنحنيات؟

    المركز المماسي هو نقطة في مستوي المنحني تكون متساوية البعد عن جميع مماسات المنحني.

  4. ما هي النتائج الرئيسية التي توصل إليها البحث؟

    النتائج الرئيسية تشمل أن مركز الدائرة هو مركز التوازن لحقل جاذبية أي منحني متجانس يحيط بها، وأن المنحنيات المحيطة بدائرة تتطابق حقول جاذبيتها في مركز الدائرة.


References used
WESTFALL Richard, « Newton », Figures de la science, Flammarion, Paris, 1994
Galileo Galilei, Dialogue sur les deux grands systèmes du monde, Paris, Seuil, 1992
K. Abdullah, Propriétés du système séculaire, thèse de doctorat de l'Observatoire de Paris, Paris 2001
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