The development of mathematical methods

An approach [1] is suggested (1995), which allows to analyse the stability of motion in the presence of spinor motions described by means of rotation (turn) tensor. The problem is that the rotation tensors are not elements of a linear space (unlike the displacement vectors). Thus the equations in variations have to be written down as a chain of equations, whose right parts depend on the previous variations in a nonlinear way. However, the obtained chain of equations allows for the exact separation of variables, i.e. the separation of the time variable.
  1. Zhilin P.A. Spin motions and stability of equilibrium configurations of thin elastic rods // Mechanics and Control. Proc. of St. Petersburg State Technical University. 1995. N 458. P. 56-73. (In Russian.)