External stability of resonances in the motion of an asymmetric rigid body with a strong magnet in the geomagnetic field

2010 ◽  
Vol 45 (1) ◽  
pp. 10-21 ◽  
Author(s):  
V. V. Lyubimov
Keyword(s):  
Rigid Body ◽  
Geomagnetic Field ◽  
External Stability ◽  
Asymmetric Rigid Body

Analytic Solution of Euler’s Equations of Motion for an Asymmetric Rigid Body

1996 ◽  
Vol 63 (1) ◽  
pp. 149-155 ◽  
Author(s):  
P. Tsiotras ◽  
J. M. Longuski
Keyword(s):  
Rigid Body ◽  
Analytic Solution ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
First Order ◽  
Symmetry Assumption ◽  
Angular Velocities ◽  
Previous Solution ◽  
First Order Correction ◽  
Asymmetric Rigid Body

The problem of the time evolution of the angular velocity of a spinning rigid body, subject to torques about three axes, is considered. An analytic solution is derived that remains valid when no symmetry assumption can be made. The solution is expressed as a first-order correction to a previous solution, which required a symmetry or near-symmetry assumption. Another advantage of the new solution (over the former) is that it remains valid for large initial conditions of the transverse angular velocities.

scholarly journals Estimation of the probability of two consecutive passages through resonance during the descent of an asymmetric rigid body in a rarefied atmosphere

2021 ◽  
Vol 2099 (1) ◽  
pp. 012066
Author(s):  
V V Lyubimov
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Rigid Body ◽  
Ordinary Differential Equations ◽  
Initial Conditions ◽  
System Of Equations ◽  
Principal Resonance ◽  
Aerodynamic Asymmetry ◽  
Asymmetric Rigid Body ◽  
Random Nature

Abstract A two-frequency nonlinear system of ordinary differential equations is considered. This system describes the perturbed motion of a rigid body with considerable asymmetry in a rarefied atmosphere. It is known that when the frequencies of this system of equations coincide, the phenomena of capture or passage through the principal resonance, which have a random nature, are possible. In this case, the probability of a passage through the resonance is calculated from the initial conditions on the separatrix. The objective of this study is to obtain an expression for estimating the probability of two consecutive passages through the resonance regions during the descent in the rarefied atmosphere of Mars of a rigid body with significant geometric and aerodynamic asymmetry.

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