Control problems for planar and spherical pendulum models have been studied by outstanding researchers; see [3-6].
Egeland, "Swinging up the spherical pendulum via stabilization of its first integrals," Automatica.
These pendulum models comprise the downward pendulum [5], horizontal pendulum [6], inverted pendulum [7], spherical pendulum [8], the flexible pendulum [9, 10], the pendulum excited by an RLC circuit based on nonlinear shaker [11], and rotating pendulum [12].
Kuang, "On the chaotic dynamics of a spherical pendulum with a harmonically vibrating suspension," Nonlinear Dynamics, vol.
The solution of nonlinear differential equations for spherical pendulum swaying requires the introduction of modern numerical computational analysis techniques.
In this work, the authors have derived two- and three-dimensional models for a spherical pendulum taking into account the linearity of transport motion.
Grigorov and Mitrev [18] have investigated a spherical pendulum dynamic model for a numerical solution of a freely suspended swinging load problem.
Mathematical descriptions of relative and absolute payload swaying motion during crane boom rotation require the introduction of design models for a spherical pendulum with a suspension point following a horizontal circular trajectory.
Applied engineering problems in the field of lifting-and-transport machines mainly deal with rectilinear or rotational motion of the spherical pendulum suspension center in determined and stochastic cases.
have implemented finite element simulation for a flexible crane structure with a spherical pendulum [34].