Mathematical modeling of the “Dzhanibekov’s effect” using the Andoyer — Deprit variables
Published: 16.10.2025
Authors: Ignatov A.I., Ermolina A.A., Petrov A.G.
Published in issue: #11(167)/2025
Category: Mechanics | Chapter: Theoretical Mchanics, Machine Dynamics
Two cases of angular motion of a rigid body relative to a point moving uniformly and rectilinearly are investigated. In the first case, the body motion is considered under the action of an external moment of potential force on the body, in the second case — in the absence of any moments. A mathematical model is compiled that describes the angular motion of the body using the Andoyer — Depri variables. The results of numerical modeling are presented under the condition that the trajectory of the end of the vector of the angular momentum of the body has a small deviation from the separatrices. This condition determines the angular motion of the body, called the “Dzhanibekov's effect”. Differences in the angular motion of the body in the presence and absence of the external moment of potential forces are shown. An analytical dependence is given that allows one to estimate the period of change in the nutation angle of the body in the absence of external moments.
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