Invariant relations for kirchhoff equations and the Kowalewski method

Abstract

The Kowalewski exponents in the problem on the motion of a solid under the Chaplygin condition are calculated (when there is a velocity-linear invariant relation). The method of calculation uses the generalizing Ioshida theorems on the Kowalewski exponents found by V.V. Kozlov. It is shown that the general solution of the equations of motion branches out in the complex time plane under the Chaplygin conditions.