The motion of a body with elastic elements around a fixed point in action-angle variables

Abstract

The motion of a mechanical system formed by a rigid rotating around a fixed point and carrying elastic rods, which undergo flexural deformation, is investigated. The asymptotic method of constructing approximate equations describing the evolution of the system motion in canonical action-angle variables is employed. The method of separating the motions and using the averaging operator enables the qualitative features of the behaviour of the system to be investigated, since, as a rule, the equations of motion of such systems cannot be integrated in explicit form.