The Holditch-Type Theorem for the Polar Moment of Inertia of the Orbit Curve in the Generalized Complex Plane |
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Authors: | Tülay Erişir Mehmet Ali Güngör Murat Tosun |
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Institution: | 1.Department of Mathematics,Sakarya University,Sakarya,Turkey;2.Department of Mathematics,Sakarya University,Sakarya,Turkey |
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Abstract: | In this study, we first calculate the polar moment of inertia of orbit curves under one-parameter planar motion in the generalized complex plane \({{\mathbb{C}_p}}\) and then give the Holditch-type theorem for \({{\mathbb{C}_p}}\): When the fixed points \({X}\) and \({Y}\) on the moving plane \({{\mathbb{K}_p} \subset {\mathbb{C}_p}}\) trace the same curve \({k}\) with the polar moment of inertia \({{T_X}}\), the different point \({Z}\) on this line segment \({XY}\) traces another curve \({{k_Z}}\) with the polar moment of inertia \({{T_Z}}\) during the one-parameter planar motion in the fixed plane \({{\mathbb{K}'_p} \subset {\mathbb{C}_p}}\). Thus, we obtain that the difference between the polar moments of inertia of these curves \({( {{T_Z} - {T_X}} )}\) depends on the only the \({p}\)-distances of this points and \({p}\)-rotation angle of the motion, \({{T_X} - {T_Z} = {\delta _p}ab.}\) |
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