Singular divergence instability thresholds of kinematically constrained circulatory systems

Static instability or divergence threshold of both potential and circulatory systems with kinematic constraints depends singularly on the constraintsʼ coefficients. Particularly, the critical buckling load of the kinematically constrained Zieglerʼs pendulum as a function of two coefficients of the constraint is given by the Plücker conoid of degree n=2. This simple mechanical model exhibits a structural instability similar to that responsible for the Velikhov–Chandrasekhar paradox in the theory of magnetorotational instability.