Construction and analysis of rational modes of rigid body motion control

DOI: 10.34759/trd-2022-124-03

Аuthors

Smirnov A. S.^*, Smolnikov B. A.^**

Peter the Great Saint-Petersburg Polytechnic University, 29, Polytechnicheskaya str., St. Petersburg, 195251, Russia

*e-mail: smirnov.alexey.1994@gmail.com
**e-mail: smolnikovba@yandex.ru

Abstract

The paper considers the motion of a rigid body under the action of a control moment, formation of which is carried out in various ways and meets the specific control goals. The main properties of the collinear control and its modified version are discussed, which lead to an increase or decrease in both kinetic energy and kinetic momentum, and as a result they allow overclocking or braking of a rigid body. Orthogonal control is also considered, which does not violate the constancy of kinetic energy and kinetic momentum and leads to a reorientation of the rigid body in space. In addition, combined control options are constructed, which have the features of both collinear and orthogonal controls in their structure. First control option allows dissipating or accumulating kinetic energy at a constant kinetic moment, and the second option, on the contrary, leads to a decrease or increase in the kinetic moment at a constant kinetic energy. Such controls can be interpreted as rational, since they are efficient, have a fairly simple structure, and are convenient for practical implementation. Moreover, physical analogies are given for the constructed control options, which make it possible to correlate their action with inertia forces, dissipative forces of external and internal friction, as well as gyroscopic forces. Based on various methods, exact analytical solutions are constructed for the mentioned modes, and these solutions describe the process of controlled motion of a rigid body and demonstrate its properties. The results obtained in the work are not only of fundamental theoretical significance, but can also be used in solving applied problems of rigid body dynamics.

Keywords:

rigid body, rational control mode, collinear control, orthogonal control, combined control

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