Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T09:26:58.083Z Has data issue: false hasContentIssue false
  • English
  • Français

On random rotations

Published online by Cambridge University Press:  01 July 2016

P. H. Roberts  and
D. E. Winch
P. H. Roberts
Affiliation:
University of Newcastle upon Tyne
D. E. Winch
Affiliation:
University of Sydney
Get access Rights & Permissions [Opens in a new window]

Abstract

A body receives a sequence of rotations through a fixed angle about an axis whose direction is arbitrary. The probability distribution governing the resulting orientation of the body is determined. The problem is generalized to the case where the axis of each individual rotation makes the same angle, Θ, with an axis fixed in the body but is otherwise random. The resulting distribution is shown, in the case , to reduce to the Roberts-Ursell distribution for random walk on a sphere. Some diffusion limits are examined.

Keywords

RANDOM WALKQUATERNIONSHYPERSPHERICAL HARMONICSDIFFUSION DISTRIBUTION
Type
Research Article
Information
Advances in Applied Probability , Volume 16 , Issue 3 , September 1984 , pp. 638 - 655
Copyright
Copyright © Applied Probability Trust 1984 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Kendall, M. E. and Moran, P. A. P. (1963) Geometrical Probability. Griffin, London.Google Scholar
Miles, R. E. (1965) On random rotations in R3. Biometrika 52, 636–639.Google Scholar
Roberts, P. H. and Ursell, H. D. (1960) Random walk on a sphere and on a Riemannian manifold. Phil. Trans. R. Soc. London A 252, 317–356.Google Scholar
Vilenkin, N. J. (1968) Special Functions and the Theory of Group Representations. Amer. Math. Soc. Providence, RI.CrossRefGoogle Scholar
Whittaker, E. T. and Watson, G. N. (1927) A Course in Modern Analysis. Cambridge University Press.Google Scholar