Yıl 2018, Cilt 1 (2018), Sayı 1, Sayfalar 1 - 6 2018-12-14

Circling-Point Curve in Minkowski Plane

Soley Ersoy [1] , Kemal Eren [2]

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The purpose of this paper is to study the circling-point curve and its degenerate cases at the initial position of motion in Minkowski plane. The first part of the paper is devoted to the determination Bottema's instantaneous invariants and trajectory of origin with respect to these invariants in Minkowski plane. The intersection points of the circling-point curve and inflection curve are called Ball points. Here the number and also the geometric location of Ball points in Minkowski plane have been determined. The fundamental geometric property of a trajectory of each point in a plane is its curvature function $\kappa$. Under consideration $\kappa = \kappa ' = \;\kappa '' = 0$, the existence conditions of Ball points in Minkowski plane have been given.

Circling-point curve, Ball point, Instantaneous Invariants, Burmester Theory
  • [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] G. R. Veldkamp, Curvature theory in plane kinematics PhD Thesis, Groningen: T.H. Delft, 1963.
  • [5] G. R. Veldkamp, Some remarks on higher curvature theory, J. Manuf. Sci. Eng., 89 (1967), 84–86.
  • [6] G. R. Veldkamp, Canonical systems and instantaneous invariants in spatial kinematics, J. Mech., 2(1967) 329–388.
  • [7] K. Eren, S. Ersoy, Cardan positions in the Lorentzian plane, Honam Math. J., 40(1), (2018) 187-198.
  • [8] K. Eren, S. Ersoy, Burmester theory in Cayley-Klein planes with affine base, J. Geom., 109(3):45 (2018).
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Orcid: 0000-0002-7183-7081
Yazar: Soley Ersoy
Kurum: Sakarya University
Ülke: Turkey


Orcid: 0000-0001-5273-7897
Yazar: Kemal Eren

Bibtex @konferans bildirisi { cpost486055, journal = {Conference Proceedings of Science and Technology}, issn = {2651-544X}, address = {Murat TOSUN}, year = {2018}, volume = {1 (2018)}, pages = {1 - 6}, doi = {}, title = {Circling-Point Curve in Minkowski Plane}, key = {cite}, author = {Ersoy, Soley and Eren, Kemal} }
APA Ersoy, S , Eren, K . (2018). Circling-Point Curve in Minkowski Plane. Conference Proceedings of Science and Technology, 1 (2018) (1), 1-6. Retrieved from http://dergipark.gov.tr/cpost/issue/41126/486055
MLA Ersoy, S , Eren, K . "Circling-Point Curve in Minkowski Plane". Conference Proceedings of Science and Technology 1 (2018) (2018): 1-6 <http://dergipark.gov.tr/cpost/issue/41126/486055>
Chicago Ersoy, S , Eren, K . "Circling-Point Curve in Minkowski Plane". Conference Proceedings of Science and Technology 1 (2018) (2018): 1-6
RIS TY - JOUR T1 - Circling-Point Curve in Minkowski Plane AU - Soley Ersoy , Kemal Eren Y1 - 2018 PY - 2018 N1 - DO - T2 - Conference Proceedings of Science and Technology JF - Journal JO - JOR SP - 1 EP - 6 VL - 1 (2018) IS - 1 SN - 2651-544X- M3 - UR - Y2 - 2018 ER -
EndNote %0 Conference Proceedings of Science and Technology Circling-Point Curve in Minkowski Plane %A Soley Ersoy , Kemal Eren %T Circling-Point Curve in Minkowski Plane %D 2018 %J Conference Proceedings of Science and Technology %P 2651-544X- %V 1 (2018) %N 1 %R %U
ISNAD Ersoy, Soley , Eren, Kemal . "Circling-Point Curve in Minkowski Plane". Conference Proceedings of Science and Technology 1 (2018) / 1 (Aralık 2018): 1-6.