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Restricting forces (“ligadure” forces)

Suppose we try to obtain the movement equation for a particle sliding on a sphere (no friction, ideal bodies...). The only forces acting on the particle are its weight and - here's my problem - a force that keeps the particle attached to the sphere*. How I am supposed to represent mathematically this kind of forces? As a restriction on the coordinates of the particle?

Thank you.

$*$ My teacher refers to this, in Spanish, as a "fuerza de ligadura". I don't have a clue on its correct translation; does ligature force make any sense?