Construction of the approximate stability equations of motion for an elastic cylindrical body under axial compressive load

A method of constructing nonlinear motion stability equations for isotropic elastic bodies is developed for cylindrical bodies of standard material of the 2nd order subjected to the action of “dead” axial compressive forces. The perturbation of the displacement vector is given by its approximate decomposition with respect to the base of tensor functions of the 1st, 2nd and 3d valences. The time-dependent tensor coefficients of the decomposition satisfy the system of ordinary differential equations. Based on the obtained equations one can investigate the balance stability of cylindrical bodies under various fixing conditions.