Instruments composed of arrangements of linear accelerometers are used to determine motion variables. With nine accelerometers, the angular rate of the instrument can be resolved algebraically rather than by the solution of a system of nonlinear differential equations. The algebraic equations consist of three quadratic forms in the angular rate and, in general, lead to multiple solutions. The number and distribution of the multiple roots have been analyzed. Examples illustrate the application of the analyses, for batch and real-time processing. Suitable algorithms have been developed and are detailed. Subjects for further study have been indicated.
Issue Section:
Research Papers
1.
Padgaonkar
, A. J.
, Krieger
, K. W.
, and King
, A. I.
, 1979, “Measurement of Angular Acceleration of a Rigid Body Using Linear Accelerometers
,” ASME J. Appl. Mech.
0021-8936, 46
, pp. 925
–930
.2.
Bulmash
, G.
, Loucks
, R.
, Muller
, P.
, and Pearson
, R.
, 1989, “Dynamics of the Nine Linear Accelerometer System for Measuring Blast Induced Target Displacements
,” ASME J. Comput. Inf. Sci. Eng.
1530-9827, 1
, pp. 179
–182
.3.
Vreeburg
, J. P. B.
, “Verification by Prony Analysis of Flat-Spin Motion From Accelerometer Data
,” IEEE Trans. Aerosp. Electron. Syst.
0018-9251, submitted.4.
Vreeburg
, J. P. B.
, 1999, “Analysis of the Data From a Distributed Set of Accelerometers, for Reconstruction of Set Geometry and Its Rigid Body Motion
,” Space Technology and Applications International Forum-1999
, M.
Genk
, ed., American Institute of Physics
, Melville, NY
, CP 458, pp. 496
–509
.5.
Goldstein
, H.
, 1988, Classical Mechanics
, 2nd ed., Addison-Wesley
, Reading, MA
.6.
Cardou
, P.
, and Angeles
, J.
, 2008, “Angular Velocity Estimation From the Angular Acceleration Matrix
,” ASME J. Appl. Mech.
0021-8936, 75
, p. 021003
.7.
Chen
, J. -H.
, Lee
, S. -C.
, and DeBra
, D. B.
, 1994, “Gyroscope Free Strapdown Inertial Measurement Unit by Six Linear Accelerometers
,” J. Guid. Control Dyn.
0731-5090, 17
(2
), pp. 286
–290
.Copyright © 2010
by American Society of Mechanical Engineers
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