On Recursive Random Prolate Hyperspheroids
Abstract
This technical note analyzes the properties of a random sequence of prolate hyperspheroids with common foci. Each prolate hyperspheroid in the sequence is defined by a sample drawn randomly from the previous volume such that the sample lies on the new surface (Fig. 1). Section 1 defines the prolate hyperspheroid coordinate system and the resulting differential volume, Section 2 calculates the expected value of the new transverse diameter given a uniform distribution over the existing prolate hyperspheroid, and Section 3 calculates the convergence rate of this sequence. For clarity, the differential volume and some of the identities used in the integration are verified in Appendix A through a calculation of the volume of a general prolate hyperspheroid.
Cite
@article{arxiv.1403.7664,
title = {On Recursive Random Prolate Hyperspheroids},
author = {Jonathan D. Gammell and Siddhartha S. Srinivasa and Timothy D. Barfoot},
journal= {arXiv preprint arXiv:1403.7664},
year = {2014}
}
Comments
11 pages, 2 figures