Asymptotical Expansions of Modified Motions of a Rigid Body.
Abstract:
Here we continue the study of power expansions of solutions to the modified system of equations, describing motions of a rigid body with a fixed point, begun in the preprints №49 and 73 (2001). We have studied all power expansions of solutions, corresponding to the edge Г7(1) (§7) and to the face Г5(2) (§8) of the polyhedron of equations of motions. In §7 we have overcome two kinds of degeneracity. In §8 we have found new cases of the integrability with respect to the fractional powers of the independent variable. We show the places of the known solutions found by Steklov, Chaplygin, Kovalevskaya, Gorjachev, Kowalevski in the entire picture and prove that all found here solutions can be expanded in power series of the time (§9).
Publication language:russian
Research direction:
Mathematical problems and theory of numerical methods
