In physics and engineering, Davenport chained rotations are three chained intrinsic rotations about body-fixed specific axes. Euler rotations and Tait–Bryan rotations are particular cases of the Davenport general rotation decomposition. The angles of rotation are called Davenport angles because the general problem of decomposing a rotation in a sequence of three was studied first by Paul B. Davenport.[1]
The non-orthogonal rotating coordinate system may be imagined to be rigidly attached to a rigid body. In this case, it is sometimes called a local coordinate system. Given that rotation axes are solidary with the moving body, the generalized rotations can be divided into two groups (here x, y and z refer to the non-orthogonal moving frame):
Generalized Euler rotations
(z-x-z, x-y-x, y-z-y, z-y-z, x-z-x, y-x-y)
Generalized Tait–Bryan rotations
(x-y-z, y-z-x, z-x-y, x-z-y, z-y-x, y-x-z).
Most of the cases belong to the second group, given that the generalized Euler rotations are a degenerated case in which first and third axes are overlapping.
^P. B. Davenport, Rotations about nonorthogonal axes
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id., at p. 482. Albrechtsen, Hanne, as cited in Zins, id., at p. 480. Davenport, Thomas H.; Laurence Prusack (1998). Working Knowledge: How Organizations...
goes into effect in South Korea". Gamasutra. Retrieved June 26, 2019. Davenport, James (September 30, 2016). "The worst bullshots in PC gaming". PC Gamer...
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Allen (Arizona to Denver), Calais Campbell (Baltimore to Atlanta), Marcus Davenport (New Orleans to Minnesota), Javon Hargrave (Philadelphia to San Francisco)...
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using area-preserving affine transformations instead of translations and rotations. The result depended on finding free groups of affine transformations...
PMID 34879190. Khoury, David S.; Steain, Megan; Triccas, James A.; Sigal, Alex; Davenport, Miles P.; Cromer, Deborah (17 December 2021). "A meta-analysis of Early...
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original newspaper article of September 15, 2012; also BBC "In Pictures: Chain of Command"; https://www.thedrive.com/the-war-zone/7300/letters-of-last...
Golden Palace on several occasions in the mid-2000s, running the series in rotation as a de facto eighth season of The Golden Girls. The show's existence is...
demolished in 1987. Government Bridge on the Mississippi River between Davenport, Iowa and Rock Island, Illinois (1896) Grand Haven GTW RR Swing Bridge...
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