Singular trajectories in the problem of simple pursuit on a manifold

A. A. Melikyan, N. V. Ovakimyan

Research output: Contribution to journalArticlepeer-review


Same problems of simple pursuit are discussed. It is shown that in such problems singular trajectories, being the envelopes of geodesic lines, can appear. The necessary condition for availability of singular motions (the set is not empty) is determined. An algorithm of singular motion construction is proposed. The Hamiltonian equations, determining these motions, are given. The problem of sufficiency of the proposed structure is numerically studied using particular examples. A straight circular cylinder and a convex cone are considered as a phase space. The calculations have shown that the singular trajectories of the players have rectilinear trajectories, which they quickly converge to.

Original languageEnglish (US)
Pages (from-to)54-62
Number of pages9
JournalPrikladnaya Matematika i Mekhanika
Issue number1
StatePublished - Jan 1991
Externally publishedYes

ASJC Scopus subject areas

  • Applied Mathematics


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