Abstract
The kinetic energy of the transient response of a harmonic oscillator is minimized by actions with a bounded current total momentum. Such a problem arises, for example, when choosing a mass flow program minimizing the kinetic energy of transfer of a satellite into a circular orbit by a reactive force having the direction of the Earth's gravitational force (see [1], p. 32). It is shown that the optimal control contains an impulse component. This leads to the violation of the optimality principle for extremals. Therefore, the synthesis procedure is based on the analysis of an auxiliary variational problem under the usual constraints on the control [2].
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