Singular divergence instability thresholds of kinematically constrained circulatory systems

• Published in: Physics letters. A Vol. 378; no. 3; pp. 147 - 152
• Main Authors: Kirillov, O.N., Challamel, N., Darve, F., Lerbet, J., Nicot, F.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.01.2014; Elsevier
• Subjects: Circulatory system; Constraints; Divergence; Engineering Sciences; Instability; Kinematic constraints; Magnetorotational instability; Material instabilities; Mathematical models; Mechanics; Non-commuting limits; Solid state physics; Stability; Static instability; Thresholds; Ziegler pendulum; Ziegler pendulum; Static instability; Magnetorotational instability; Material instabilities; Kinematic constraints; Non-commuting limits
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2013.10.046

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. •Static instability threshold of a system with kinematic constraints can be singular.•The singular surface is the Plücker conoid for the constrained Ziegler pendulum.•The Plücker conoid governs switching between buckling loads.•This provides a mechanical analogue to the Velikhov–Chandrasekhar paradox in MHD.