On a Spacelike Line Congruence Which Has the Parameter Ruled Surfaces as Principal Ruled Surfaces

In this paper, explicit expressions were improved for timelike ruled surfaces with the similarity of hyperbolic dual spherical movements. From this, the well known Hamilton and Mannhiem formulae of surfaces theory are attained at the hyperbolic line space. Then, by employing the E. Study map, a new timelike Plücker conoid is immediately founded and its geometrical properties are examined. In addition, via the height dual function, we specified the connection among the timelike ruled surface and the order of contact with its timelike Disteli-axis. Lastly, a classification for a timelike line to be a stationary timelike Disteli-axis is attained and explained in detail. Our findings contribute to a deeper realization of the cooperation between hyperbolic spatial movements and timelike ruled surfaces, with potential implementations in fields such as robotics and mechanical engineering.

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A Study on a Spacelike Line Trajectory in Lorentzian Locomotions

Almoneef,

Abdel-Baky

2023

Symmetry

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In this study, we establish a novel Lorentzian interpretation of the Euler–Savary (E−S) and Disteli (Dis) formulae. Subsequently, we proceed to establish a theoretical structure for a Lorentzian torsion line congruence which is the spatial symmetry of the Lorentzian circling-point dual curve, in accordance with the principles of the kinematic theory of spherical locomotions. Further, a timelike (Tlike) torsion line congruence is defined and its spatial equivalence is examined. The findings contribute to an enhanced comprehension of the interplay between axodes and Lorentzian spatial movements, which has possible significance in various disciplines, such as the fields of robotics and mechanical engineering.

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On a Spacelike Line Congruence Which Has the Parameter Ruled Surfaces as Principal Ruled Surfaces

Cited by 5 publications

References 7 publications

On the kinematic-geometry of one-parameter Lorentzian spatial movement

On the kinematic-geometry of one-parameter Lorentzian spatial movement

One-Parameter Hyperbolic Dual Spherical Movements and Timelike Ruled Surfaces

A Study on a Spacelike Line Trajectory in Lorentzian Locomotions

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