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


Abstract in English

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.

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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