The motion of a rigid body in a fluid under the action of central newtonian attractive forces

Abstract

The structure of the forces and moments which arise when a rigid body moves in an unbounded volume of an ideal incompressible fluid under the action of central Newtonian attractive forces is discussed, the equations of motion are written in explicit form, their first integrals are indicated and the properties of these integrals are investigated. The problem of possible simplifications in the formulation of the problem is investigated, based on an analogy with the classical “satellite approximation” and which hold when the translational velocity of the body can be regarded as being independent of its rotational motion. The question of the existence and stability of steady motions, in this case relative equilibria, is investigated in the satellite approximation.