title: Spherical pendulum small oscillations for slewing crane motion.
abstract: The present paper focuses on the Lagrange mechanics-based description of small oscillations of a spherical pendulum with a uniformly rotating suspension center. The analytical solution of the natural frequencies' problem has been derived for the case of uniform rotation of a crane boom. The payload paths have been found in the inertial reference frame fixed on earth and in the noninertial reference frame, which is connected with the rotating crane boom. The numerical amplitude-frequency characteristics of the relative payload motion have been found. The mechanical interpretation of the terms in Lagrange equations has been outlined. The analytical expression and numerical estimation for cable tension force have been proposed. The numerical computational results, which correlate very accurately with the experimental observations, have been shown.
authors: Manufacturing Processes and Automation Engineering Department, Engineering Automation Faculty, Donbass State Engineering Academy, Shkadinova 72, Donetsk Region, Kramatorsk 84313, Ukraine.
authors: Alexander V
authors: AV
authors: Perig
authors: Department of Technical Mechanics, Engineering Automation Faculty, Donbass State Engineering Academy, Shkadinova 72, Donetsk Region, Kramatorsk 84313, Ukraine.
authors: Alexander N
authors: AN
authors: Stadnik
authors: Department of Technical Mechanics, Engineering Automation Faculty, Donbass State Engineering Academy, Shkadinova 72, Donetsk Region, Kramatorsk 84313, Ukraine.
authors: Alexander I
authors: AI
authors: Deriglazov
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical