# Reduction problem with constraints on the total momenta of the controls:PMM vol. 39, n≗2, 1975, pp. 216–224

- Authors
- Journal
- Journal of Applied Mathematics and Mechanics 0021-8928
- Publisher
- Elsevier
- Publication Date
- Volume
- 39
- Issue
- 2
- Identifiers
- DOI: 10.1016/0021-8928(75)90141-0

## Abstract

Abstract We examine the reduction problem for the trajectories of a conflict-controlled linear stationary system in a specified neighborhood of the equilibrium position. The actions of the opponents are restricted by constraints on the magnitude of the total momenta of controls. Such constraints admit of stepwise displacements along directions capable of piercing the target set. The considered problem is reduced, by means of the generalized impulse calculus, to an auxiliary one which is solvable by the methods in [1]. The obtained impulse extremal construction depends upon the initial position and admits of stepwise motions in the sliding mode. In the general case it is necessary for the party interested in the reduction to know the part of the trajectory realized up to the instant of making a decision. In Sect. 1 we examine the problem of the encounter of two material points of variable mass, while in Sect. 2 the reduction problem for a multidimensional conflict-controlled stationary system with a nonsingular matrix is considered.

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