We consider the torque-free rotation of a rigid body with three distinct moment of inertia values and angular velocity components. As can be seen in the Dzhanibekov and tennis racket phenomena, rotations about the largest and smallest principal moments of inertia create stable rotations. However, when rotating about the principal intermediate moment of inertia, an unstable rotation is produced that leads to the basis of this phenomena. In this publication, the above phenomena are examined and explained analytically and applied to a satellite system to observe the change in trajectory as the solar panels and reflectors are deployed. To begin the derivation, the Euler torque-free equations for a rotating rigid body are formulated using the moving frame method. The derived equations are then non-dimensionalized and a complete analytical solution, including an expression for the non-dimensional period, is presented. Second, we further look at the limiting axisymmetric cases and examine the effect as the intermediate moment of inertia is varied. Lastly, the analytical expressions are compared with the numerical simulation to validate the results. The complete solution is then summarized and shown to clearly prove that the conservation of angular momentum is indeed preserved in the phenomena.
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ASME 2016 International Mechanical Engineering Congress and Exposition
November 11–17, 2016
Phoenix, Arizona, USA
Conference Sponsors:
- ASME
ISBN:
978-0-7918-5054-1
PROCEEDINGS PAPER
An Analytical and Geometrical Study of the Dzhanibekov and Tennis Racket Phenomena Available to Purchase
Oscar Rios,
Oscar Rios
University of California, San Diego, La Jolla, CA
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Takeyuki Ono,
Takeyuki Ono
University of California, San Diego, La Jolla, CA
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Hidenori Murakami,
Hidenori Murakami
University of California, San Diego, La Jolla, CA
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Thomas J. Impelluso
Thomas J. Impelluso
Bergen University College, Bergen, Norway
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Oscar Rios
University of California, San Diego, La Jolla, CA
Takeyuki Ono
University of California, San Diego, La Jolla, CA
Hidenori Murakami
University of California, San Diego, La Jolla, CA
Thomas J. Impelluso
Bergen University College, Bergen, Norway
Paper No:
IMECE2016-65570, V04AT05A049; 10 pages
Published Online:
February 8, 2017
Citation
Rios, O, Ono, T, Murakami, H, & Impelluso, TJ. "An Analytical and Geometrical Study of the Dzhanibekov and Tennis Racket Phenomena." Proceedings of the ASME 2016 International Mechanical Engineering Congress and Exposition. Volume 4A: Dynamics, Vibration, and Control. Phoenix, Arizona, USA. November 11–17, 2016. V04AT05A049. ASME. https://doi.org/10.1115/IMECE2016-65570
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