[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c180087

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)

Publication Information

Communications of the Korean Mathematical Society / v.34, no.1, 2019 , pp. 333-349 More about this Journal

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.

Keywords

E. Study's map; axodes; line congruence; Disteli's formula;

Citations & Related Records

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