To the analytical dynamic analysis of non-linear parametric systems with gears

In contrast to the mathematical methods of solution of the linear dynamic problems are the analytical solution methods and the analysis of non-linear at that the analysis of the time heteronymous, i.e. parametrical, problems more complicated and difficult. In these systems can occur the various dynamic behaviour, where appear, in the certain sensible areas of the tuning, the new often unexpected phenomena, such as the patterns of the solution ambiguity, the bifurcation and the splitting of the resonance characteristics, the change over the regular motions into the irregular, up to the motions with deterministic chaotic character etc. The above mentioned and the another phenomena can occur at the more precise physical modelling in the category of the high-parametrical, i.e. in the light high-speed structures, for example in the aeronautical propjets, where today the revolutions of the driving turbines are reaching the 80000 rpm. For the analysis of the mentioned phenomena of the relative motion in gear mesh of the kinematic pairs of pseudoplanetary systems with the split power flow is in the paper applied the method of the transformation of boundary-value non-linear differential problem into the integral-differential problem with the solving cores in the form of splitting Green's resolventes.