The fundamental principles of the gyroscope theory contain the system of the inertial torques generated by the rotating mass of the spinning disc that interrelated by the ratio of its angular velocities rotation around axes. The action of the centrifugal, common inertial Coriolis forces and the change in the angular momentum generate the system of inertial torques. These four dynamical components make up the system of the eight torques acting simultaneously on the spinning disc. They manifest their action in gyroscopic effects. The ratio of the precessed motions of the gyroscope presents one of the gyroscopic effects around axes of rotation. The known mathematical model for this ratio contains an error that was corrected in this work.
References
[1]
Cordeiro, F.J.B. (2015) The Gyroscope. CreateSpace, Nevada.
[2]
Greenhill, G. (2015) Report on Gyroscopic Theory. Relink Books, Fallbrook.
[3]
Scarborough, J.B. (2014) The Gyroscope Theory and Applications. Nabu Press, London.
[4]
Weinberg, H. (2011) Gyro Mechanical Performance: The Most Important Parameter. Technical Article MS-2158, Analog Devices, Norwood, 1-5.
[5]
Hibbeler, R.C. and Yap, K.B. (2013) Mechanics for Engineers-Statics and Dynamics. 13th Edition, Prentice Hall, Pearson, Singapore.
[6]
Gregory, D.R. (2006) Classical Mechanics. Cambridge University Press, New York.
[7]
Taylor, J.R. (2005) Classical Mechanics. University Science Books, California.
[8]
Aardema, M.D. (2005) Analytical Dynamics. Theory and Application. Academic/ Plenum Publishers, New York.
[9]
Liang, W.C. and Lee, S.C. (2013) Vorticity, Gyroscopic Precession, and Spin-Cur-vature Force. Physical Review D, 87, Article ID: 044024. https://doi.org/10.1103/PhysRevD.87.044024
[10]
LeMoyne, R., Mastroianni, T., McCandless, C., Currivan, C., Whiting, D. and Tomycz, N. (2018) Implementation of a Smartphone as a Wearable and Wireless Accelerometer and Gyroscope Platform for Ascertaining Deep Brain Stimulation Treatment Efficacy of Parkinson’s Disease through Machine Learning Classification. Advances in Parkinson’s Disease, 7, 19-30.
[11]
Yong, C.Y., Sudirman, R., Mahmood, N.H. and Chew, K.M. (2013) Motion Classification Using Proposed Principle Component Analysis Hybrid K-Means Clustering. Engineering, 5, 25-30. https://doi.org/10.4236/eng.2013.55B006
[12]
Crassidis, J.L. and Markley, F.L. (2016) Three-Axis Attitude Estimation Using Rate-Integrating Gyroscopes. Journal of Guidance, Control, and Dynamics, 39, 1513-1526. https://doi.org/10.2514/1.G000336
[13]
Nanamori, Y. and Takahashi, M. (2015) An Integrated Steering Law Considering Biased Loads and Singularity for Control Moment Gyroscopes. AIAA Guidance, Navigation, and Control Conference, Kissimmee, 5-9 January 2015. https://doi.org/10.2514/6.2015-1091
[14]
Jewett, J. and Serway, R.A. (2018) Physics for Scientists and Engineers. 10th Edition, Cengage Learning, Boston.
[15]
Knight, R.D. (2016) Physics for Scientists and Engineers: A Strategic Approach with Modern Physics. 4th Edition, Pearson, London.
[16]
Usubamatov, R. (2018) Inertial Forces Acting on Gyroscope. Journal of Mechanical Science and Technology, 32, 101-108. https://doi.org/10.1007/s12206-017-1211-0
[17]
Usubamatov, R. (2015) Mathematical Model for Gyroscope’s Gimbal Motions. 4th International Conference on Advances in Engineering Sciences & Applied Mathematics (ICAESAM’2015), Kuala Lumpur, 8-9 December 2015, 41-44.
[18]
Usubamatov, R. (2020) Theory of Gyroscope Effects for Rotating Objects. Springer, Singapore. https://doi.org/10.1007/978-981-15-6475-8
