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Geometric interpretation of Curvature Circles in Minkowski Plane

Year 2019, Volume: 2 Issue: 3, 205 - 208, 30.12.2019

Kemal Eren Soley Ersoy

Abstract

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

Supporting Institution

Sakarya University

Thanks

This research is partially supported by BAPK of Sakarya University project number 2019-8-28-186

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] 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.

Year 2019, Volume: 2 Issue: 3, 205 - 208, 30.12.2019

Kemal Eren Soley Ersoy

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] 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.
There are 11 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Kemal Eren This is me 0000-0001-5273-7897

Soley Ersoy This is me 0000-0002-7183-7081

Publication Date December 30, 2019
Acceptance Date December 5, 2019
Published in Issue Year 2019 Volume: 2 Issue: 3

Cite

APA Eren, K., & Ersoy, S. (2019). Geometric interpretation of Curvature Circles in Minkowski Plane. Conference Proceedings of Science and Technology, 2(3), 205-208.
AMA Eren K, Ersoy S. Geometric interpretation of Curvature Circles in Minkowski Plane. Conference Proceedings of Science and Technology. December 2019;2(3):205-208.
Chicago Eren, Kemal, and Soley Ersoy. “Geometric Interpretation of Curvature Circles in Minkowski Plane”. Conference Proceedings of Science and Technology 2, no. 3 (December 2019): 205-8.
EndNote Eren K, Ersoy S (December 1, 2019) Geometric interpretation of Curvature Circles in Minkowski Plane. Conference Proceedings of Science and Technology 2 3 205–208.
IEEE K. Eren and S. Ersoy, “Geometric interpretation of Curvature Circles in Minkowski Plane”, Conference Proceedings of Science and Technology, vol. 2, no. 3, pp. 205–208, 2019.
ISNAD Eren, Kemal - Ersoy, Soley. “Geometric Interpretation of Curvature Circles in Minkowski Plane”. Conference Proceedings of Science and Technology 2/3 (December 2019), 205-208.
JAMA Eren K, Ersoy S. Geometric interpretation of Curvature Circles in Minkowski Plane. Conference Proceedings of Science and Technology. 2019;2:205–208.
MLA Eren, Kemal and Soley Ersoy. “Geometric Interpretation of Curvature Circles in Minkowski Plane”. Conference Proceedings of Science and Technology, vol. 2, no. 3, 2019, pp. 205-8.
Vancouver Eren K, Ersoy S. Geometric interpretation of Curvature Circles in Minkowski Plane. Conference Proceedings of Science and Technology. 2019;2(3):205-8.
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