A.A. Piskovatsky – Ph.D.(Eng.), Design Engineer, PJSC
«Dolgoprudny Research and Production Enterprise»
In 1803 Louis Poinseau put forward the initial provisions of the static for the transformation of forces acting on an absolutely solid body (ASB). The static conversion data was later used to solve dynamics problems.
This transformation is based on the principle of determining the change in angular position and angular velocity without taking into account the centers relative to which these changes occurred. As the speed parameters of the MA increase due to this assumption adopted for the described conversion, methodological errors of determination of parameters of rotational motion of the MA increase. The purpose of the article is to increase the accuracy of prediction of flight parameters in the tasks of analysis and mathematical simulation of maneuvering aircraft by determining the basis of a method that does not use the principle of determining the change of angular position and angular velocity without taking into account the centers relative to which these changes occurred, as well as the movement of pairs parallel to itself.
The main method of investigation used in the article is the method of geometric representations and analytical conclusions on these representations.
The article provides arguments on the appearance of errors in determining the angular velocity and angular acceleration of the MA without determining the axes (centers) around which these parameters operate.
In order to eliminate errors determined by bringing external forces acting on the aircraft to the MA center of mass, arguments are given on the need to determine the centers relative to which angular acceleration acts and angular speed is created, the angular position of the MA changes.
It is determined that if there is angular velocity without errors, the velocity vector cannot be brought to the arbitrary pole, and if there is angular acceleration, the acceleration vector cannot be brought to the arbitrary pole without errors.
The article demonstrates the method of determining the instantaneous centers of action of angular acceleration and angular speed by building figures of acceleration and speed and finding parameters of rotary motion of the MA, which allows to more accurately determine the solution of the problem of flight dynamics of the MA.
The acceleration distribution shows the relationship: the greater the difference between the linear acceleration vectors of the MA measured at the individual points of the MA, to bigger angular acceleration MA is subject to those, the inclination of distribution of its linear acceleration is more,
the provision of an instant axis of action of angular acceleration of MA is closer to those to the center of mass of MA, the radius more curvature of a trajectory of flight of MA is less.
It has been suggested and proved that in the known acceleration distribution, although it is possible to divide motion into translational and rotational motion of the MA relative to any pole, the equivalent transformation is only the division relative to the axis passing through the point of application of the net external forces acting on the MA.
Thus, in order to improve prediction accuracy in solving problems of analysis and mathematical simulation of flight parameters of maneuvering aircraft, it is necessary to exclude transformation of movement of pair (forces) parallel to itself.
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