String length constraint ($L(q_1,\dots ,q_n)=l$)

The holonomic constraint obtained by summing the straight and curved segment lengths of a taut massless inextensible string and setting the result equal to its fixed length $l$. Differentiation gives ${\sum }_i(\partial L/\partial q_i){\dot{q}}_i=0$, a relation between the permitted velocities. A slack string does not impose this equality on endpoint separation.