General Mathematics, Vol. 8, nr. 1-2, pp. 11-37, 2000
Aurora Crăciunaş -- Some considerations concerning
the rotary motion of a rigid body around the mass center
Abstract:
We make a presentation of the tangent fibre bundle of the group of the orthogonal transforms and, on this fibre bundle, we construct
a riemannian structure whose metric is defined by the intermedium
of the kinetic energy of rotation.
Corresponding to this structure we calculate the Cristoffel’s symbols of second kind to
obtain the equations of the geodesics and we look for an orthogonal basis in this structure
such that the equations of the geodesics should coincide with the Euler’s equations.
We identify these three directions with the central axes of the rigid body and we show that the movement of these three directions
cannot be considered with respect to an absolute frame in the given structure of the
riemannian variety. Consequently the frame that we chose to represent the central axes of the rigid body has
a continuous movement, ((47),2), the angular velocity passing, periodically, through the same values but with respect to a moving
frame called frame "of observations".
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