Andrey A. Piskovatsky¹

1  PJSC «Dolgoprudny Research and Production Enterprise» (Dolgoprudny, Russia) 1

 e4rt@mail.ru

The article is devoted to the study of the transformation of the force vector by moving it along the line of its action – one of the methods proposed by Louis Poinsot in the treatise «The Beginnings of Statics» for solving statics problems. Since the publication of the treatise «New Theory of Rotation of Bodies», this transformation of statics was used by L. Poinsot in solving problems of motion dynamics of an absolutely solid body (ASB). A feature of using all statics transformations is that they are justified when taking the possibility of moving axes relative to which there is a change in the angular position in time and a change in the angular velocity of the ASB parallel to itself.

Unlike this principle, in the previous article by the author, on the analysis of the motion of an aircraft maneuvering with angular acceleration (MA), which can be adopted by the ASB, it is proved that at the current moment for its rotational movement in the inertial coordinate system (CS) there is a single position of the instantaneous center, relative to which the angular acceleration of this MA in this CS is determined without errors. Based on this evidence, it is necessary to examine how to limit the movement of the force vector along its line of action at the acting angular acceleration of the MA so that the position of the instantaneous center relative to which the angular acceleration of the MA changes does not change.

The purpose of the article is to increase the accuracy of prediction of flight parameters of a manoeuvring aircraft with angular acceleration in the tasks of analysis, mathematical modeling and flight control by determining restrictions on the use of force vectors acting on MAs along their line of action.

According to the results of research, the article proved that the movement of force vectors applied to MAs along their line of action leads to methodological errors in determining the moment of external forces acting on MAs. The results of the studies are presented in the form of an analysis of the movement states of ASB (including MAs) and two theorems that have been consistently proved. The proof of the stated theorems made it possible to formulate the corresponding consequences from them.

Thus, according to the results of studies for an aircraft maneuvering with angular acceleration, the need for vectors acting on it to exclude the use of forces: moving parallel to itself the axis of action of the moment of action of these forces and moving these force vectors along their line of action.

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