Open AccessAttraction basins in the generalized Kapitsa’s problem
Author(s) -
Н. Ф. Морозов,
Аlexander K. Belyaev,
П. Е. Товстик,
Т. М. Товстик,
Т. П. Товстик
Publication year - 2019
Publication title -
doklady akademii nauk. rossijskaâ akademiâ nauk
Language(s) - English
Resource type - Journals
ISSN - 0869-5652
DOI - 10.31857/s0869-56524875502-506
Subject(s) - attraction , position (finance) , inverted pendulum , action (physics) , vibration , harmonic , structural basin , stability (learning theory) , pendulum , harmonic potential , physics , classical mechanics , mathematics , geology , control theory (sociology) , nonlinear system , computer science , acoustics , paleontology , economics , quantum mechanics , philosophy , linguistics , control (management) , finance , machine learning , artificial intelligence
Stability of vertical position of an inverted pendulum under action of support vibration as well as the attraction basin of this position is considered. In addition to the classic Kapitsa problem for the harmonic vibration of support, the poly-harmonic and random vibration of support is investigated. The condition of stability of vertical position is determined and the attraction basin of this stable position is studied.