Investigation of the process of stabilization of the rotational axis of the lifting body by the pendulum autobalancer

Authors

DOI:

https://doi.org/10.15587/1729-4061.2016.63955

Keywords:

lifting body, pendulums, motion stability, spacecraft, passive autobalancer, damper

Abstract

The paper investigates the conditional stability of the basic steady motions of the spatial model of an isolated system, consisting of a rotating lifting body, a particle, creating its static unbalance and two identical mathematical pendulums, mounted on a longitudinal axis of the lifting body and moving in the plane of the static unbalance, the relative motion of which is hindered by the viscous resistance forces. It is found that in the case where unbalance is present and pendulums can correct it with a certain margin, there is one basic motion. In the absence of unbalance, there is a one-parameter family of basic motions. In the case of maximum unbalance, which can be corrected by pendulums, there is one basic motion, but it generates a pseudo family of basic motions. Also, it is revealed that some basic motions, if isolated, or a family or a pseudo family of basic motions is conditionally asymptotically stable. In the absence of unbalance, the presence of a single zero root of the characteristic equation does not affect the stability of a one-parameter family of basic motions and is responsible for the transition from one steady motion of a family to another. In the case of maximum unbalance, the presence of a single zero root of the characteristic equation does not affect the stability of the basic motion and is responsible for the transition from one steady motion of a pseudo family to another. Transition processes are oscillatory-damped.

Author Biography

Vladimir Pirogov, Kirovograd National Technical University 8 University ave., Kirovograd, Ukraine, 25030

Сandidate of physical and mathematical sciences, Associate professor

Department of machine parts and applied mechanics

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Published

2016-04-23

How to Cite

Pirogov, V. (2016). Investigation of the process of stabilization of the rotational axis of the lifting body by the pendulum autobalancer. Eastern-European Journal of Enterprise Technologies, 2(7(80), 49–63. https://doi.org/10.15587/1729-4061.2016.63955

Issue

Vol. 2 No. 7(80) (2016): Applied mechanics

Section

Applied mechanics

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Copyright (c) 2016 Vladimir Pirogov

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