NDLI: A new kinematic theorem for rotational motion

Content Provider	IEEE Xplore Digital Library
Author	Blankinship, K.
Copyright Year	2004
Description	Author affiliation: Navigation Syst. Group, Boeing Integrated Defense Syst., Midwest City, OK, USA (Blankinship, K.)
Abstract	The Goodman-Robinson theorem (ASME Jour. of App. Mech., vol.25, p, 210-213, 1968), used to explain kinematic drift in strapdown attitude algorithms due to coning motion, can be thought of as an integral form of the rotation vector differential equation. This theorem states that, in the absence of instrument errors, the delta-theta count of a rate-integrating-type gyro is equal to the time integral of the angular velocity component along the gyro sensitive axis, plus the area that the sensitive axis traces out on a sphere of unit radius. This paper utilizes the Darboux frame from differential geometry to obtain an expression for the area term in the Goodman-Robinson formula. It turns out that this term is equal to the time integral of the component along the gyro sensitive axis of the angular velocity of the angular velocity of the sensitive axis, plus exterior angle terms. The results of this paper provide a geometric explanation of how movement of the direction of the angular velocity vector contributes to kinematic drift.
Sponsorship	IEEE Aerospace & Electron. Syst. Soc
Starting Page	285
Ending Page	295
File Size	442100
Page Count	11
File Format	PDF
ISBN	0780384164
DOI	10.1109/PLANS.2004.1309007
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2004-04-26
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Kinematics Angular velocity Differential equations Geometry Gyroscopes Navigation Cities and towns Integral equations Instruments History
Content Type	Text
Resource Type	Article

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