On the Computation of Functionals Over Sample Paths of a Randomly Rotating Rigid Body

✍ Scribed by Yaakov Yavin; Menahem Friedman

• Publisher: Elsevier Science
• Year: 1977
• Tongue: English
• Weight: 569 KB
• Volume: 303
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(77)90031-x

✦ Synopsis

This paper deals with the computation of the values of two functionals which are defined over the sample paths of a randomly rotating rigid body. It is assumed that the body is subjected to two dinerent kinds of perturbation. The first kind of perturbation is represented by the standard Wiener process and the second kind by a homogeneous process with independent increments, finite second-order moments, mean zero and no continuous sample functions. In order to measure quantitatively the stochastic stability of the body's motion, two functionals are defined over its sample paths. It is shown that each of these functionals is a solution to a corresponding partial integro-difierential equation. A numerical procedure for the solution of these equations is suggested, and its efficiency and applicability are demonstrated with examples.