On integrability of a heavy rigid body sinking in an ideal fluid

Abstract

We consider a rigid body possessing 3 mutually perpendicular planes of symmetry, sinking in an ideal fluid. We prove that the general solution to the equations of motion branches in the complex time plane, and that the equations consequently are not algebraically integrable. We show that there are solutions with an infinitely-sheeted Riemannian surface. (2000). 70E99, 70H07. Mathematics Subject Classification