Locking constraints for elastic rods and a curvature bound for spatial curves

The paper presents necessary conditions for curves in R³ subject to the nonholonomic constraint of an upper bound for curvature and suitable boundary conditions. The proof essentially uses a reformulation of the problem by means of framed curves. The Euler–Lagrange equations for nonlinearly elastic Cosserat rods subject to a general class of locking constraints is derived by similar methods. Mathematics Subject Classification (2000) 49K15, 51M16, 74B20, 74K10