Optimization of Oscillation Damping Modes of a Spatial Double Pendulum: 1. Formulation of the Problem

Smirnov, Alexey S.; Smolnikov, B. A.

doi:10.1134/s1063454122020133

Cited by 4 publications

(4 citation statements)

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“…This is precisely the characteristic feature of internal dissipation [Smirnov, and Smolnikov, 2022]. We note that expressions similar in structure were obtained earlier in the study of the motion of a spherical pendulum with internal friction in its rod [Smirnov, and Smolnikov, 2019], as well as in a similar problem for a gyroscopic pendulum [Smolnikov, 2008]. In addition, the problem of the motion of a rigid body with a cavity filled with a viscous fluid deserves attention, where the phenomenon of continuous energy dissipation also took place while maintaining the momentum integral [Chernousko, Akulenko, and Leshchenko, 2017].…”

Section: Entering the Regular Precession Modesupporting

confidence: 74%

“…(38) These equations are similar to the equations of motion of a spherical pendulum written in gimbal angles, which was required to be shown [Smirnov, and Smolnikov, 2019]. We note that if it is necessary to trace in more detail the process of the system entering the mode of motion of a spherical pendulum, then we can consider small deviations, for which equations (38) take the form:…”

Section: Complete Suppression Of Movements Of a Gyroscopic Pendulummentioning

confidence: 98%

“…To do this, we can use the analogy with internal friction, which requires a detailed discussion. It is clear that such a mode of controlled motion will be of particular interest, since the issue of taking into account internal friction during oscillations of various mechanical systems is extremely relevant [Smirnov, and Smolnikov, 2019;Smirnov, and Smolnikov, 2022]. To this end, we construct the control in such a way that the values p and ω 3 are constant, and the total mechanical energy E decreases over time, and its dissipation would stop on the circular motion of the center of mass of the system.…”

Section: Entering the Regular Precession Modementioning

confidence: 99%

“…Taking into account formulas ( 5) and ( 6), we find the relations between the Cartesian coordinates of the center of mass of a gyroscopic pendulum and the gimbal angles in the following form [Smirnov, and Smolnikov, 2019]:…”

Section: Introductionmentioning

confidence: 99%

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Controlled motion modes of a gyroscopic pendulum in a gimbal suspension

Smirnov,

Sarvilov

2023

CAP

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The issues of controlling the motion of a gyroscopic pendulum fixed in a gimbal suspension and having three degrees of freedom are discussed in the paper. It is proposed to use physical analogies and correlate their action with the dissipative forces of external viscous friction, friction in gimbal joints and internal friction in the pendulum rod, as well as inertial forces and gyroscopic forces to form the control torques in gimbal joints. Six modes of controlled movement of the system are considered, which allow achieving various goals. It is shown that it is possible to completely suppress the motions of a gyroscopic pendulum, switch it to the mode of a spherical or physical pendulum, enter the mode of rotation around a fixed vertical axis, bring it to the mode of regular precession, and also strengthen or weaken the gyroscopic structure of the motion equations. The discussion of these modes of controlled motion is accompanied by the construction of motion equations both within the framework of the original nonlinear model and for simplified linear or weakly nonlinear models. The obtained results are theoretically interesting and may be useful for specific practical applications in the field of gyroscopic technology.

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Section: Entering the Regular Precession Modesupporting

confidence: 74%

Section: Complete Suppression Of Movements Of a Gyroscopic Pendulummentioning

confidence: 98%

Section: Entering the Regular Precession Modementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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