Rotational dynamics for the spherical body with displaced center of mass

Authors

  • П. П. Шигорін Eastern European National University Ukrainian, Ukraine

Keywords:

spherical body, dynamics, rotational motion, stable state

Abstract

In the article has been considered the theoretical description of the rotational mechanics for the spherical body with displaced center of mass (SBDCM). In terms of the general equations for dynamics of a rigid body the equations of translational and rotational motion for SBDCM was constructed. The solution of these equations near turning-over point has been analyzed. In particular, has shown that the parameter x, that describe dependence of rotation frequency on the inclination angle, evolves from the initial value x0 = Сn0 through the oscillations near value x–. When angle increases q, the amplitude of oscillation decreases. Near state q = p the amplitude of oscillation will increase again. The critical rotation frequency, when body turning from stable state to unstable was calculated too.

Author Biography

П. П. Шигорін, Eastern European National University Ukrainian

Candidate of Physical and Mathematical Sciences

References

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Aleshkevich V. A., Dedenko L.G., Karavaev V.A. (1997). Lekcii po mehanike tverdogo tela [Lectures on rigid body mechanics]. Moscow, MGU, 98p. (in Russian).

Karapetyan A. V. (1991). “Qualiative investigation of the dynamics of a top on a plane with friction”. J. Appl. Math. Mech. 55: 563–565.

Rauch-Wojciechowski S., Skoldstam M., and Glad T. (2005). “Mathematical Analysis of the Tippe Top” Regul. Chaotic Dyn. 10: 333–362.

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Published

2015-10-08

Issue

Vol. 18 No. 3 (2015)

Section

Dynamics and Strength of Machines

License

Copyright (c) 2015 П. П. Шигорін

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