Singular divergence instability thresholds of kinematically constrained circulatory systems

Abstract : Static instability or divergence threshold of both potential and circulatory systems with kinematic constraints depends singularly on the constraints’ coefficients. Particularly, the critical buckling load of the kinematically constrained Ziegler’s 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.
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Oleg N. Kirillov, Noël Challamel, Félix Darve, Jean Lerbet, François Nicot. Singular divergence instability thresholds of kinematically constrained circulatory systems. Physics Letters A, Elsevier, 2014, 378 (3), pp.147-152. ⟨10.1016/j.physleta.2013.10.046⟩. ⟨hal-02442219⟩

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