Acta Scientific Computer Sciences

Research Article Volume 4 Issue 8

Corrected Mathematical Model for the Top Motions with the Eccentric Mass

Ryspek Usubamatov*

Kyrgyz State Technical University After I. Razzakov, Bishkek, Kyrgyzstan

*Corresponding Author: Ryspek Usubamatov, Kyrgyz State Technical University After I. Razzakov, Bishkek, Kyrgyzstan.

Received: March 04, 2022; Published: July 18, 2022


The top toy is a simplest gyroscopic device which mathematical model for a motion is not well-presented in the known publications. Recent investigations have shown the gyroscope properties are more complex. The external force applied on a gyroscope generates of the interrelated centrifugal and Coriolis forces of the mass elements, the change in the angular momentum, and centre mass of the spinning rotor. These system of torques acting around two axes of the spinning top express the basic principles of the gyroscope theory. The system of the inertial torques formulate the mathematical models for the nutation of the top toy with the eccentric mass. This manuscript presents the mathematical model for the top nutation in terms of vibration analysis.

Keywords: Gyroscope Theory; Property; Top Nutation


  1. Armenise MN., et al. “Advances in Gyroscope Technologies”. Springer-Verlag Berlin and Heidelberg GmbH and Co. KG, Berlin, (2010).
  2. Deimel RF. “Mechanics of the Gyroscope.” Dover Publications Inc. New York (2003).
  3. Greenhill G. “Report on Gyroscopic Theory”. General Books LLC, London (2010).
  4. Scarborough JB. “The Gyroscope Theory and Applications”. Nabu Press, London (2011).
  5. Hibbeler RC. “Engineering Mechanics - Statics, and Dynamics”. 12th Prentice-Hall, Pearson, Singapore, 2010.
  6. Gregory DR. “Classical Mechanics”. Cambridge University Press, New York, (2006).
  7. Taylor JR. “Classical Mechanics”. University Science Books, California, USA, (2005)
  8. Aardema MD. “Analytical Dynamics”. Theory and Application. Academic/Plenum Publishers, New York, (2005).
  9. Jewett J and Serway “Physics for Scientists and Engineers”. Cengage Learning, 10 ed. USA, Boston, (2018).
  10. Knight R D. “Physics for Scientists and Engineers: A Strategic Approach with Modern Physics”. Pearson, 4 ed., UK, London, (2016).
  11. Perry J. “Spinning Tops and Gyroscopic Motions”. Literary Licensing, LLC, NV USA, (2012).
  12. Klein F and Sommerfeld A. “The theory of the top. I – IV”. New York, NY: Springer, Birkhäuser, (2008):2008-2014.
  13. Usubamatov R. “Theory of gyroscopic effects for rotating objects”. Springer, Singapore (2020).
  14. Usubamatov R and Allen D. “Corrected Inertial Forces of Gyroscopic Effects”. Advances in Mathematical Physics (2022): 7.
  15. Usubamatov R and Omorova A. “A Mathematical Model for Top Nutation Based on Inertial Forces of Distributed Masses”. Mathematical Problems in Engineering (2018).
  16. Usubamatov R. “Corrected Internal Torques of Gyroscopic Effects”. Online Journal of Robotics and Automation Technology2 (2022):1-4.
  17. Usubamatov R and Bergander M. “Physics of deactivation of gyroscopic inertial forces”. Journal of Mechanical Engineering Research 1(2021): 30-36.


Citation: Ryspek Usubamatov. “Corrected Mathematical Model for the Top Motions with the Eccentric Mass". Acta Scientific Computer Sciences 4.8 (2022): 102-106.


Copyright: © 2022 Ryspek Usubamatov. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.


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