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Investigation of possibilities of estimating the rotation parameters using a number of optical images


V.V. Lavrov

At present, optical observations of space objects can get their pictures on long time intervals, comparable to the duration of a accompaniment object. In some cases, recorded images suggest the rotation of the object. Then the repetitive images of some elements of construction can be identified on the frames, the orientation of this images varies depending on the time and rotation parameters of the object. Any clearly identified on the image elements can be used as these identifying characteristic form, in particular: long rod, the size and direction of which can be recorded at different times, elongated objects bodies, planar elements, such as solar panels or antennas. We consider the rotation of the object «Okean-1». The images are taken from the shot a film at one of the telescopes, these frames shows the movement of the object. The image of the object in each frame is actually a projection of the object on the picture plane or screen. In the framework of the regular precession of the most common axisymmetric object rotation of the center of mass, the projection of the axis of symmetry of the object onto a plane perpendicular to the direction of the angular momentum vector, will be a circle with a radius equal to the length of the object along the symmetry axis, multiplied by the sine of the angle of mutation, the special case of «tumbling» (the flat rotation object) – just this length. In another case, when viewed from the direction perpendicular to the angular momentum vector, the point located at the end of the object axis, will move along a segment of a straight line. Thus, the projection of a circle, at which point at the end of the axis of the object moves, at some arbitrary plane is an ellipse with parameters depending on the orientation of the angular momentum vector and the plane, if during the leading they are fixed relative to each other. The same picture plane, which we see on the screen (in screen coordinates), can significantly change its position in space due to relative motion of the orbital motion, and a telescope, located on the surface of a rotating Earth. In connection with this rod coordinates must be converted into a fixed reference system, in which the orientation of the angular momentum vector will be determined. Converting the coordinates of the bar image on the screen and approximating their harmonic functions depending on the time, we can construct a circle that the object bar describes in the selected fixed coordinate system and projection of this circle on the coordinate plane of the adopted system of coordinates. The results of calculations confirm the possibility of using the proposed approach for estimating the parameters of motion relative to the center of mass for the totality of its optical images, in which we can provide a key element to the construction of apparatus, and to monitor the temporal evolution of the orientation of this element in the image frames.

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