Abstract
The paper summarises attempts which have been made to derive general, simple and stable formulae of adequate precision for the reduction of observations to the extremal positions of oscillations which are simple harmonic or near-simple harmonic. A fallacy in the thirty-five year old Schuler Mean is pointed out and general formulae are offered for the reduction of observations for any constant damping, within the range0<f≤1.
Similar content being viewed by others
References
F. KOHLRAUSCH: Praktische Physik, 20th. ed., 1955, 1, 129.
M. SCHULER: Die Berechnung der Gleichgewichtslage von gemessenen Schwingungen auf Grund der Fehlertheorie, Zeit. für Angewandte Math. und Mech., 12, 1932, 152–156.
G.B. LAUF: Adjustment and Precision of Gyro-theodolite Observations, Paper 5/17, Third South African National Survey Conference, January 1967.
H.S. WILLIAMS and G.E. BELLING: The Reduction of Gyro-theodolite Observations, Survey Review, XIX, 146, 184–190, October 1967.
H.S. WILLIAMS and G.E. BELLING: Quasi-harmonic Patterns of Pendulous Gyroscopes During Protracted Oscillation, Tijdschrift voor Kadaster en Landmeetkunde, 83e jaargang, 5, 269–284, October 1967.
H.S. WILLIAMS: Rigorous Adjustment of Observations of Weakly-Damped Near-Simple Harmonic Motions (To be published).
Author information
Authors and Affiliations
Additional information
An erratum to this article is available at http://dx.doi.org/10.1007/BF02524848.
Rights and permissions
About this article
Cite this article
Williams, H.S. Predictor stabilisation of reduction formulae for observations of heavily-damped simple harmonic motions. Bull. Geodesique 89, 333–343 (1968). https://doi.org/10.1007/BF02525708
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02525708