trihedron


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Related to trihedron: tetrahedron

tri·he·dron

 (trī-hē′drən)
n. pl. tri·he·drons or tri·he·dra (-drə)
A figure formed by three planes meeting at a point. Also called trihedral.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

trihedron

(traɪˈhiːdrən)
n, pl -drons or -dra (-drə)
(Mathematics) a figure determined by the intersection of three planes
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014
Translations

trihedron

nDreiflächner m, → Trieder nt
Collins German Dictionary – Complete and Unabridged 7th Edition 2005. © William Collins Sons & Co. Ltd. 1980 © HarperCollins Publishers 1991, 1997, 1999, 2004, 2005, 2007
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[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.
Axes i is tangent to the Earth, j is orthogonal to i and runs against the gravity, and k is orthogonal to both i and j, setting up a right-handed trihedron. The model is illustrated in Figure 2.
If we consider any orthogonal trihedron as {[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]}, we can write their derivative formulas as follows:
[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.
Aha, quivering before me in the mist, The Sacred Trihedron, emblematic of the one point in hyper space that has no coordinates.
The trihedron [mathematical expression not reproducible], N represents a moving frame of M along the initial geodesic.