Asymptotics for kinetic energy of ideal fluid with two moving spheres of variable radii near their contact

摘要

The problem on motion of two spheres of variable radii in an ideal liquid is considered. Spheres are near to contact. However, derivatives in co-ordinates have logarithmic divergence at a small split between spheres. Because of this we have difficulties of calculations of motion of spheres on the Lagrange equations near to contact. To overcome them by the specially developed method, the asymptotic decomposition of series is searched in case of a small split between spheres. Asymptotic decomposition of coefficients of kinetic energy is calculated in this way.