INFLUENCE OF NONLINEAR COUPLINGS ON THE BEHAVIOUR OF THE SOLUTION OF THE EQUATIONS OF MOTION OF A MECHANICAL SYSTEM.

The subject matter of this analysis is the influence of nonlinear couplings on the behaviour of the solution of the equations of motion of a mechanical system which may be subdivided into sub-systems non-linearly coupled. The conditions for the motion of the sub-systems to be bounded and capable of being made arbitrarily small are established. Another subject of discussion are bands which can be constructed making use of the solution of a suitable set of linear differential equations, and which contain solution of the subset considered. The width of these bands depends on the estimated values of the nonlinear coupling functions. For synthesis these bands can be made arbitrarily narrow, which means in practice rejection of the nonlinear couplings. The results discussed have been obtained by methods of integral inequalities.