A differential pursue game with velocity-control players which are the points of 3D space is considered. The points accomplish simple motions along 2D conical surface, at any moment of time they have opportunity to choose arbitrary, tangential to cone direction for their velocity vectors restricted by constants in value. The initial game comprising the dynamic equations of the forth order is shown to be reduced to 2D one by using self-similar variables. Motions of players along interlink geodesy line are shown to be optimum ones in the main area of phase space. In another space area any player moves along its own geodesy line. The third type of optimum motions is found to take place for some values of parameters.
|Original language||English (US)|
|Number of pages||11|
|Journal||Prikladnaya Matematika i Mekhanika|
|State||Published - Sep 1991|
ASJC Scopus subject areas
- Applied Mathematics