Singular trajectory in the problem of simple pursuit on a manifold

A. A. Melikyan, N. V. Ovakimyan

Research output: Contribution to journalArticle

Abstract

Games with at most two minimal geodesics connecting two points in their phase space (manifold) are considered. It is shown that singular trajectories - envelopes of geodesics - may develop in such games. A necessary condition for the existence of singular motions (non-emptiness of the set (3.5)) is derived as a certain requirement from the geometrical properties of the phase manifold of the game. An algorithm to construct the singular motions is proposed and the Hamiltonian equations describing these motions are given. The sufficiency of the proposed construction is investigated numerically for particular examples. The paper generalizes and extends the previous study /1/.

Original languageEnglish (US)
Pages (from-to)48-55
Number of pages8
JournalJournal of Applied Mathematics and Mechanics
Volume55
Issue number1
DOIs
StatePublished - 1991
Externally publishedYes

ASJC Scopus subject areas

  • Modeling and Simulation
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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