Barycentric coordinates in the equilibrium problem of a heavy rough triangle suspended on a pin

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A planar equilibrium problem of a heavy homogeneous thin wire triangle suspended on a thin horizontal nail is considered. The existence of equilibrium positions and their dependence on the coefficient of friction and the lengths of the sides of the triangle are studied under the assumption of the presence of a dry friction force acting between the triangle and the nail. The problem is solved in barycentric coordinates associated with the vertex system of the triangle in question. The equilibrium condition is written in a form that allows a cyclic shift of the indices of the quantities included in it to obtain an equilibrium condition for any of the sides of the triangle with which it contacts the nail.

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Е. Nikonova

FRC CSC RAS

编辑信件的主要联系方式.
Email: nikonova.ekaterina.a@gmail.com
俄罗斯联邦, Moscow

参考

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2. Fig. 1. Wire triangle A1A2A3. P13, P23 are the boundary points of the set of non-isolated equilibria on the side A1A2.

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