[mathematical expression not reproducible] is pointing north, [mathematical expression not reproducible] is perpendicular to [mathematical expression not reproducible] and pointing nadir, and [mathematical expression not reproducible] is forming a clockwise trihedron. Body axes are defined by subindex B.
[10] expressed a family of surfaces from a given spacelike or timelike asymptotic curve using the Frenet trihedron frame of the curve in Minkowski 3-space [E.sup.3.sub.1].
where O is the center of mass of the Earth, the axis O[xi] running to the perigee, the axis O[zeta] pointing to the angular momentum, and the axis O[eta] making a direct trihedron. The radius vector of the satellite is given by
A trihedron ([T.sub.0]; [e.sub.1], [e.sub.2], [e.sub.3]), with a proper origin [T.sub.0] ([x.sub.0],[y.sub.0],[z.sub.0]) ~ (1 : [x.sub.0] : [y.sub.0] : [z.sub.0]), is orthonormal in pseudo-Galilean sense iff the vectors [e.sub.1], [e.sub.2], [e.sub.3] have the following form: [e.sub.1] = (1, [y.sub.1], [z.sub.1]), [e.sub.2] = (0, [y.sub.2], [z.sub.2]), [e.sub.3] = (0, [epsilon][z.sub.2], [epsilon][y.sub.2]), with [y.sup.2.sub.2] = [z.sup.2.sub.2] = [delta], where each of [epsilon], [delta] is +1, or -1.
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