Kemal EREN, Soley ERSOY

Geometric interpretation of Curvature Circles in Minkowski Plane

ISSN: 2651-544X
Başlangıç: 2018
Yayıncı: Murat TOSUN

In this study, we investigate the geometric interpretation of the curvature circles of motion at the initial position in Minkowski plane. We consider the equations of the circling-point and centering-point curves of one-parameter motion in Minkowski plane and then determine the positions of these curves relative to each other.

Keywords:

Centering-point curve Circling-point curve, Minkowski plane,

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[1] O. Bottema, On instantaneous invariants, Proceedings of the International Conference for Teachers of Mechanisms, New Haven (CT): Yale University, 1961, 159–164.
[2] O. Bottema, On the determination of Burmester points for five distinct positions of a moving plane; and other topics, Advanced Science Seminar on Mechanisms, Yale University, July 6-August 3, 1963.
[3] O. Bottema, B. Roth, Theoretical Kinematics, New York (NY), Dover, 1990.
[4] B. Roth, On the advantages of instantaneous invariants and geometric kinematics, Mech. Mach. Theory, 89 (2015), 5–13.
[5] F. Freudenstein, Higher path-curvature analysis in plane kinematics, ASME J. Eng. Ind., 87 (1965), 184–190.
[6] F. Freudenstein and G. N. Sandor, On the Burmester points of a plane, ASME J. Appl. Mech., 28 (1961), 41–49.
[7] G. R. Veldkamp, Curvature theory in plane kinematics [Doctoral dissertation], Groningen: T.H. Delft, 1963.
[8] G. R. Veldkamp, Some remarks on higher curvature theory, J. Manuf. Sci. Eng., 89 (1967), 84–86.
[9] G. R. Veldkamp, Canonical systems and instantaneous invariants in spatial kinematics, J. Mech., 2 (1967) 329–388.
[10] K. Eren, S. Ersoy, Circling-point curve in Minkowski plane, Conference Proceedings of Science and Technology, 1(1), (2018), 1–6.
[11] K. Eren, S. Ersoy, A comparison of original and inverse motion in Minkowski plane, Appl. Appl. Math., Special Issue No.5 (2019), 56–67.