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Year 2018, Volume: 1 Issue: 1, 1 - 6, 14.12.2018

Soley Ersoy Kemal Eren

Abstract

References

  • [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).

Circling-Point Curve in Minkowski Plane

Year 2018, Volume: 1 Issue: 1, 1 - 6, 14.12.2018

Soley Ersoy Kemal Eren

Abstract

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.

Keywords

Circling-point curve Ball point Instantaneous Invariants Burmester Theory

References

  • [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).
There are 8 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Soley Ersoy 0000-0002-7183-7081

Kemal Eren 0000-0001-5273-7897

Publication Date December 14, 2018
Acceptance Date December 4, 2018
Published in Issue Year 2018 Volume: 1 Issue: 1

Cite

APA Ersoy, S., & Eren, K. (2018). Circling-Point Curve in Minkowski Plane. Conference Proceedings of Science and Technology, 1(1), 1-6.
AMA Ersoy S, Eren K. Circling-Point Curve in Minkowski Plane. Conference Proceedings of Science and Technology. December 2018;1(1):1-6.
Chicago Ersoy, Soley, and Kemal Eren. “Circling-Point Curve in Minkowski Plane”. Conference Proceedings of Science and Technology 1, no. 1 (December 2018): 1-6.
EndNote Ersoy S, Eren K (December 1, 2018) Circling-Point Curve in Minkowski Plane. Conference Proceedings of Science and Technology 1 1 1–6.
IEEE S. Ersoy and K. Eren, “Circling-Point Curve in Minkowski Plane”, Conference Proceedings of Science and Technology, vol. 1, no. 1, pp. 1–6, 2018.
ISNAD Ersoy, Soley - Eren, Kemal. “Circling-Point Curve in Minkowski Plane”. Conference Proceedings of Science and Technology 1/1 (December 2018), 1-6.
JAMA Ersoy S, Eren K. Circling-Point Curve in Minkowski Plane. Conference Proceedings of Science and Technology. 2018;1:1–6.
MLA Ersoy, Soley and Kemal Eren. “Circling-Point Curve in Minkowski Plane”. Conference Proceedings of Science and Technology, vol. 1, no. 1, 2018, pp. 1-6.
Vancouver Ersoy S, Eren K. Circling-Point Curve in Minkowski Plane. Conference Proceedings of Science and Technology. 2018;1(1):1-6.
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