Nikolai paradox

The Nikolai paradox [1 - 7] is analysed (1993-2005). The paradox appears when a rod is subjected to the torsion by means of the torque applied to its end. The experiment shows that the torsion torque stabilises the rod, which is in the major contradiction with the theory. It is shown [6], that one may avoid the mentioned paradox if to choose a special constitutive equation for the torque. The torque has to depend in a special way on the rotational velocity. This dependence is not related to the existence (or absence) of the internal friction in the rod.
  1. Zhilin P.A., Sergeyev A.D. Twisting of an elastic cantilever rod by a torque subjected at a free end. St. Petersburg State Technical University. 1993. 32 p. (In Russian.)
  2. Zhilin P.A., Sergeyev A.D. Experimental investigation of the stability of a cantilever rod under torsion deforming // Mechanics and Control. Proc. of St. Petersburg State Technical University. 1993. N 446. P. 174-175. (In Russian.)
  3. Zhilin P.A., Sergeyev A.D. Equilibrium and stability of a thin rod subjected to a conservative moment // Mechanics and Control. Proc. of St. Petersburg State Technical University. 1994. N 448. P. 47-56. (In Russian.)
  4. Zhilin P.A., Sergeyev A.D., Tovstik T.P. Nonlinear theory of rods and its application // Proc. of XXIV Summer School - Seminar “Nonlinear Oscillations in Mechanical Systems”. St. Petersburg. 1997. P. 313-337. (In Russian.)
  5. Zhilin P.A. Advanced problems in mechanics. Selection of articles. V. 1. St. Petersburg. Edition of IPME RAS. 2006. 306 p. (In Russian.)
  6. Zhilin P.A. Advanced problems in mechanics. Selection of articles. V. 2. St. Petersburg. Edition of IPME RAS. 2006. 271 p.
  7. Zhilin P.A.Applied mechanics. Theory of thin elastic rods. Tutorial book. St. Petersburg State Polytechnical University. 2007. 101 p. (In Russian.)