Ruled surfaces with constant Disteli-axis

Nadia Alluhaibi; Nadia Alluhaibi

doi:10.3934/math.2020491

AIMS Mathematics

2020, Volume 5, Issue 6: 7678-7694. doi: 10.3934/math.2020491

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Research article

Ruled surfaces with constant Disteli-axis

Nadia Alluhaibi ^,

Department of Mathematics, Science and Arts College, Rabigh Campus, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia

Received: 09 July 2020 Accepted: 03 September 2020 Published: 27 September 2020
MSC : 53A04, 53A05, 53A17

This work develops the kinematic-geometry for ruled surfaces by using the analogy with spherical kinematics. This provides the ability to compute set of curvature functions which define the local shape of ruled surfaces. Hence, the well known equation of the Plücker's conoid has been obtained and its kinematic-geometry are examined in details. Finally, a characterization for a line trajectory to be a constant Disteli-axis is derived, and investigated.
- Blaschke frame,
- E. study map,
- line complex,
- Disteli-axis
Citation: Nadia Alluhaibi. Ruled surfaces with constant Disteli-axis[J]. AIMS Mathematics, 2020, 5(6): 7678-7694. doi: 10.3934/math.2020491

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Abstract

This work develops the kinematic-geometry for ruled surfaces by using the analogy with spherical kinematics. This provides the ability to compute set of curvature functions which define the local shape of ruled surfaces. Hence, the well known equation of the Plücker's conoid has been obtained and its kinematic-geometry are examined in details. Finally, a characterization for a line trajectory to be a constant Disteli-axis is derived, and investigated.

References

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