Circling-Point Curve in Minkowski Plane

Yıl 2018, Cilt: 1 Sayı: 1, 1 - 6, 14.12.2018

Soley Ersoy Kemal Eren

Öz

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.

Anahtar Kelimeler

Circling-point curve, Ball point, Instantaneous Invariants, Burmester Theory

Kaynakça

• [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).