Analysis of the Euler-Poisson Equations by Methods of Power Geometry.
Here we consider the Euler-Poisson system of equations, describing motions of a rigid body with a fixed point, in the case B ≠ C, x0 ≠ 0, y0 = z0 = 0. The N.Kowalewski transformation tranforms it into a system of two ODE. By means of the three-dimensional Power Geometry, for solutions the last system, we compute all families of power and power-logarithmic asymptotics and expansions. We point out the sets of parameters A, B, C where expansions of all families (a) have not the complex power exponents, (b) have no logarithms, (c) have rational power exponents only. We discuss the existence of the additional first integral. We also compute characteristics of the corresponding families of expansions of solutions to the Euler-Poisson equations.
Mathematical problems and theory of numerical methods