CONTROL OF THE BENDING OF THE TORSO BY CHANGING THE DEPENDENCE OF THE ANGLE OF RISING OF ITS BACK RIB

A spatial curve can be specified by two natural equations: the dependence of the curvature and the dependence of the twist on the length of its arc. If such a curve is taken as the edge of the torso turn, then its bending can be controlled by changing the curvature of the curve, since the curvature does not change. However, in practice, such bending is difficult to implement, since there is no simple transition from the natural equations of the spatial curve to the parametric ones. Such a transition requires numerical methods for solving a system of differential equations. It is possible to approach the solution of this question in a different way, namely to replace the dependence of the twist on the length of the arc of the curve with the dependence of the angle of elevation also on the length of the arc of the curve. In this case, the formulas for the transition from natural equations to parametric ones are greatly simplified and in some cases do not require numerical integration. The article uses just such an approach for constructing torsos. The parametric equations of the torso in its general form are presented, in which the turning edge is a spatial curve, given by the dependence of the curvature and the angle of elevation on the length of its arc. It is shown that by changing the regularity of the angle of elevation, the process of bending the torso can be controlled. At the same time, the expression of the first quadratic form was found, which does not include the dependence of the angle of elevation of the turning edge, but only the dependence of its curvature. This indicates that it is possible to transform the back edge in different ways, that is, to bend the torso, and at the same time the first square shape remains unchanged. A well-known example of the bending of a helicoid torso by a discrete change in the elevation angle of its reverse rib is given. Torso-helicoid bending by changing the elevation angle of the turning rib according to the linear law is also demonstrated. Numerical methods were used for this. The resulting torso is no longer a torso of the same inclination of the generators. An example of bending of the torso is also given, in which the curvature and the angle of elevation of the turning rib are variable dependences on the length of the arc. They are selected in such a way that they allow obtaining intermediate positions of the torso during its bending with the help of equations in the final form. Examples are given, visualization of the obtained results is carried out.