Partially averaged equations of motion of an axisymmetric shell (Q2754761)

For introducing small parameter into equations of projectile motion, the following procedure of numerical normalization is applied. As new scales of phase variables and functions, that enter equations of motion, characteristic values of their absolute values are taken. After that, dimensionless functions of order 1 and numeric coefficients at them are separated in equations of motion. The latter are represented as powers of the number \(\varepsilon_0 = 0.1\) and then \(\varepsilon_0\) is replaced by a small parameter \(\varepsilon\). In the paper, the linearized system with small parameter is written as a subsystem of equations of progressive motion and longitudinal rotation. Forces of gravity, aerodynamic forces and moments are taken into account. Using an averaging procedure, new equations of motion, averaged in the fast phase of angular oscillations, are derived and their asymptotic error is analyzed.