Evolution of motion of a solid suspended on a thread in a homogeneous gravity fieldстатья
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Дата последнего поиска статьи во внешних источниках: 28 июля 2021 г.
Аннотация:The plane motion of a solid in a uniform gravity field is studied. The solid is suspended ona weightless inextensible thread, which remains stretched during the motion. It is assumed that thelength of the thread is large and the distance from the point of solid suspension to its center ofgravity is small. The equations of motion are presented as equations of a system with one rapidlyrotating phase. This system is analyzed using classical perturbation theory and KAM theory. It isshown that for all values of time, the movement differs little from the slow oscillations of thethread in the vicinity of the descending vertical and the solid rotation relative to the suspension pointwith an almost constant angular velocity. The measure of the set of motions, different from the abovemotions, is exponentially small.