Accelerated method for the computer calculation of a nonlinear oscillatory system

A method is developed for the accelerated calculation of a system of ordinary differential equations describing fast quasi-periodic motions. The initial system of equations is transformed into a system whose fast integrable variables have increased oscillation periods. It is shown that the zeroth terms of the asymptotic expansions of the two systems are equal, which assures a precise determination of the variables of the initial system. The case of near-resonance is examined, and the method is applied to the modeling of the motion in the atmosphere of a flight vehicle with a slight axial asymmetry.