About the Presence of Irregular Precession Motions in a Symmetric Euler Gyroscope

P.K. Plotnikov

About the Presence of Irregular Precession Motions in a Symmetric Euler Gyroscope

P.K. Plotnikov * §

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About the Presence of Irregular Precession Motions in a Symmetric Euler Gyroscope

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Abstract

Annotation-It is generally accepted that the only type of motion present in a symmetric Euler gyroscope (SEG) is regular precession. This paper proves that regular precession is not the only type of motion present, but corresponds only to the well-known initial coordinated Euler angles. At any other initial angles, motions that differ from regular precession occur. In the article, the problem is solved analytically in two stages: first, angular velocities of the gyroscope are determined using differential dynamic equations, at the second stage, as a result of integration of differential matrix kinematic and differential matrix Poisson equations (both with periodic coefficients), final relations about the SEG motion with arbitrary initial Euler angles are derived. Periodic coefficients are the SEG angular velocities that are found as a solution to the dynamic equations. From the obtained general formulas, special formulas of regular precession for particular coordinated initial Euler angles that coincide with the well-known ones are derived.

References

14 Cites in Article

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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

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No ethics committee approval was required for this article type.

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How to Cite This Article

P.K. Plotnikov. 2020. "About the Presence of Irregular Precession Motions in a Symmetric Euler Gyroscope". Global Journal of Research in Engineering - D: Aerospace Science GJRE-D Volume 20 (GJRE Volume 20 Issue D1).

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GJRE Volume 20 Issue D1

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Journal Specifications

Crossref Journal DOI 10.17406/gjre

Print ISSN 0975-5861

e-ISSN 2249-4596

Keywords

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Classification

GJRE-D Classification FOR Code: 090199

Submission ReceivedDecember 14, 2019
Peer Review Double Blind
Handling Editor
Accepted January 4, 2020
Published January 15, 2020

Version of record

v1.2

Issue date

August 27, 2020

Language

English

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