Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON THE CURVATURE THEORY OF A LINE TRAJECTORY IN SPATIAL KINEMATICS

  • Abdel-Baky, Rashad A. (Department of Mathematics Sciences Faculty for Girls King Abdulaziz University)
  • Received : 2018.03.08
  • Accepted : 2018.07.19
  • Published : 2019.01.31
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Abstract

The paper study the curvature theory of a line-trajectory of constant Disteli-axis, according to the invariants of the axodes of moving body in spatial motion. A necessary and sufficient condition for a line-trajectory to be a constant Disteli-axis is derived. From which new proofs of the Disteli's formulae and concise explicit expressions of the inflection line congruence are directly obtained. The obtained explicit equations degenerate into a quadratic form, which can easily give a clear insight into the geometric properties of a line-trajectory of constant Disteli-axis with the theory of line congruence. The degenerated cases of the Burmester lines are discussed according to dual points having specific trajectories.

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