Some problems relating to the stability of motion of a body of variable composition, with one stationary point, in a newtonian force field

1974 ◽  
Vol 10 (3) ◽  
pp. 305-310
Author(s):  
P. P. Vcherashnyuk ◽  
V. A. Eremenko
Keyword(s):  
Force Field ◽  
Stationary Point ◽  
Variable Composition ◽  
Stability Of Motion ◽  
Newtonian Force ◽  
The Stability ◽  
Newtonian Force Field

scholarly journals The Stability of Certain Motion of a Charged Gyrostat in Newtonian Force Field

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
A. A. Elmandouh ◽  
Fatimah H. Alsaad
Keyword(s):  
Force Field ◽  
Equations Of Motion ◽  
Sufficient Conditions ◽  
Newtonian Force ◽  
Hamilton System ◽  
Principal Axes ◽  
Axis Parallel ◽  
The Stability ◽  
Permanent Rotations ◽  
Newtonian Force Field

This work aims to study the stability of certain motions of a rigid body rotating about its fixed point and carrying a rotor that rotates with constant angular velocity about an axis parallel to one of the principal axes. This motion is presumed to take place due to the combined influence of the magnetic field and the Newtonian force field. The equations of motion are deduced, and moreover, they are expressed as a Lie–Poisson Hamilton system. The permanent rotations are calculated and interpreted mechanically. The sufficient conditions for instability are presented employing the linear approximation method. The energy-Casimir method is applied to gain sufficient conditions for stability. The regions of linear stability and Lyapunov stability are illustrated graphically for certain values of the parameters.

Dynamics of a double rotating system of bodies in a Newtonian force field

1975 ◽  
Vol 11 (1) ◽  
pp. 43-49
Author(s):  
V. A. Grobov ◽  
V. V. Sivenyuk
Keyword(s):  
Force Field ◽  
Rotating System ◽  
Newtonian Force ◽  
Newtonian Force Field
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