Abstract
In this paper, during one-parameter closed planar homothetic direct motions, the formula of kinetic energy is expressed. Then we show the relation between the formula of kinetic energy and the Steiner formula. We investigate some properties of closed planar homothetic motions. These motions appear between two coordinate systems, fixed and moving (direct motion). Finally, we show how the results can be applied to experimentally measured motions. As an example, we consider a motion of winch in the sagittal direction. We obtain the formula of kinetic energy for the motion of winch during one-parameter closed planar homothetic direct motions.
Highlights
Jacob Steiner established some properties of the area of a path of a point for a geometrical object rolling on a line and making a complete turn
The Steiner formula describes the dependence of the area of a curve, determined by a closed motion of one point, on the position of this point [1]
During one-parameter closed planar homothetic motions, the expression of the Steiner formula was calculated relative to fixed coordinate system
Summary
Jacob Steiner established some properties of the area of a path of a point for a geometrical object rolling on a line and making a complete turn. The Steiner formula describes the dependence of the area of a curve, determined by a closed motion of one point, on the position of this point [1]. The Steiner area formula and the Holditch theorem during one-parameter closed planar homothetic motions were expressed by A. During one-parameter closed planar homothetic motions, the expression of the Steiner formula was calculated relative to fixed coordinate system.
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