This paper deals with non conservative mechanical systems subjected to non conservative positional forces and leading to non symmetric tangential stiffness matrices. The geometric degree of nonconservativity of such systems is then defined as the minimal number $\ell$ of kinematic constraints necessary to convert the initial system into a conservative one. The issue of finding this number and of describing the set of corresponding kinematic constraints is reduced to a linear algebra problem. This index $\ell$ of nonconservativity is the half of the rank of the sew symmetric part $K_a$ of the stiffness matrix $K$ that is always an even number. The set of constraints is extracted from the eigenspaces of the symmetric matrix $K_a^2$. Several examples including the well-known Ziegler column illustrate the results.