Objects Changing the Spatial Orientation of a Solid Body by Using Mobile Mass
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ROL SYSTEMS OF MOVING OBJECTS
Objects Changing the Spatial Orientation of a Solid Body by Using Mobile Mass A. M. Shmatkov Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526 Russia e-mail: [email protected] Received February 18, 2020; revised February 21, 2020; accepted March 30, 2020
Abstract—Formulas are obtained that make it possible to realize a predetermined motion of a rigid body with respect to its center of mass in a coordinate system with this center and translating axes. It is shown that there are two significantly different cases. In the first case, the point should always be in a certain plane, which not only makes it possible to implement any required movement from this class but also allows us to use the ambiguity of the solution so that, for example, the point always moves along the same path in the specified plane. In the second case, the solution turns out to be unique and the material point should have, generally speaking, a separate spatial trajectory for each given program of reorientation of a rigid body. Moreover, in this case only those motions that satisfy the found condition can be realized.
DOI: 10.1134/S1064230720040139
INTRODUCTION The vast majority of technical devices capable of moving in terrestrial conditions have special moving parts that directly interact with the environment: wheels, tracks, propellers, legs, etc. They are located outside the body, which entails all sorts of difficulties. If the external environment is aggressive, these structural elements are at increased risk of damage, and increased resistance to external influences leads to an increase in both the cost of the product itself and the cost of its operation. If the movement should occur in a vulnerable environment (for example, inside the human body), these parts are an increased danger. Therefore, it is desirable to create devices with propulsors enclosed inside a sealed enclosure, the surface of which is much easier to adapt to external conditions. Problems of a different kind arise when creating spacecraft (see, for example, [1, 2]). The latter, as a rule, use jet engines to change their orientation in space. These engines need fuel, the delivery of which into space is expensive. Note that the difficulty consists not so much in providing the energy necessary for reorientation as in a significant mass of the required working medium. Energy can be obtained from solar panels or, say, from an onboard nuclear reactor, and the working medium, for example, for satellites that function for a long time, must be put into orbit at launch. Alternative methods for solving the orientation problem are based, in particular, on the use of gyrostabilizers. However, in order to use them, heavy structures need to be delivered into orbit and for years ensure constant rotation of massive elements at a high speed. Therefore, it is of interest to develop new methods for changing the orientation of spacecraft without using jet propulsion and continuously moving parts. Sets of problems, related
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