Open AccessThe study of the motion of a gyroscope without rotational symmetry
Author(s) -
Florina-Carmen Ciornei,
Stelian Alaci,
Radu Dumitru Pentiuc,
Carmen Bujoreanu,
O. T. Rusu
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/568/1/012018
Subject(s) - gyroscope , moment of inertia , rotational symmetry , principal axis theorem , motion (physics) , inertia , rotation (mathematics) , symmetry (geometry) , rotation around a fixed axis , rotary inertia , classical mechanics , equations of motion , physics , dynamics (music) , euler's equations , angular velocity , mathematics , mechanics , geometry , acoustics , quantum mechanics
In rigid dynamics theory the gyroscope has a special role, as one of the bodies with the most complex motion, having three degrees of freedom. As consequence of the complexity of the motion is the fact that only for three situations, the equations of motion can be analytically integrated. For all the three situations, it is assumed that the principal moments of inertia (PMI) with respect to the principal axes that are normal to the rotation axes, are equal, condition fulfilled by the shape of body of revolution of the gyroscope. The paper analyses the case when the two principal moments of inertia are unequal. The equations of motion are numerically integrated for different values of the ratio between the two PMI. The effect of the disparity between the two PMI upon the motion of the gyroscope is proved by comparison with the motion of the axisymmetric gyroscope, both obtained by numerical integration.