Stochastic Hill's equations for the study of errant rocket burns in orbit

Martin Ostoja Starzewski, James M. Longuski

Research output: Contribution to journalArticle

Abstract

The problem of errant rocket burns in low Earth orbit is of growing interest, especially in the area of safety analysis of nuclear powered spacecraft. The development of stochastic Hill's equations provides a rigorous mathematical tool for the study of such errant rocket maneuvers. These equations are analyzed within the context of a theory of linear dynamical systems driven by a random white noise. It is established that the trajectories of an errant rocket are realizations of a Gauss-Markov process, whose mean vector is given by the solution of a deterministic rocket problem. The time-dependent covariance matrix of the process is derived in an explicit form.

Original languageEnglish (US)
Pages (from-to)295-303
Number of pages9
JournalCELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
Volume54
Issue number4
DOIs
StatePublished - Dec 1 1992
Externally publishedYes

Keywords

  • Hill's equations
  • diffusion processes
  • rendezvous
  • rocket maneuvers
  • stochastic differential equations

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

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