On the invariant motions of rigid body rotation over the fixed point, via Euler angles

摘要

The generalized Euler case (rigid body rotation over the fixed point) isdiscussed here: - the center of masses of non-symmetric rigid body is assumedto be located at the equatorial plane on axis Oy which is perpendicular to themain principal axis Ox of inertia at the fixed point. Such a case was presentedin the rotating coordinate system, in a frame of reference fixed in therotating body for the case of rotation over the fixed point (at given initialconditions). In our derivation, we have represented the generalized Euler casein the fixed Cartesian coordinate system; so, the motivation of our ansatz isto elegantly transform the proper components of the previously presentedsolution from one (rotating) coordinate system to another (fixed) Cartesiancoordinates. Besides, we have obtained an elegantly analytical case of generaltype of rotations; also, we have presented it in the fixed Cartesian coordinatesystem via Euler angles.