This study aims to show how to obtain the curvature of the ellipsoid depending on azimuth angle. The curvature topic is quite popular at an interdisciplinary level. It can be to the friends of geometry, geodesy, satellite orbits in space, in studying all sorts of elliptical motions (e.g., planetary motions), curvature of surfaces and concerning eye-related radio-therapy treatment, for example the anterior surface of the cornea is often represented as ellipsoidal in form. On the calculation of the curvature, there is a famous Euler formula for rotating ellipsoid that everyone knows. Let θ be the angle, in the tangent plane, measured clockwise from the direction of minimum curvature κ1. Then the normal curvature κn (θ) in direction θ is given by κn (θ) = κ1 cos2θ + κ2 sin2θ = κ1 + (κ2 - κ1) cos2θ I wonder how can a formula for a triaxial ellipsoid? So we started to work. And we finally found the formula for the triaxial ellipsoid.
| Published in | Landscape Architecture and Regional Planning (Volume 2, Issue 2) |
| DOI | 10.11648/j.larp.20170202.13 |
| Page(s) | 61-66 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2017. Published by Science Publishing Group |
General Ellipsoid, Normal Section Curve, Principal Curvatures, Gaussian Curvature, Mean Curvature
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APA Style
Sebahattin Bektas. (2017). Curvature of the Ellipsoid with Cartesian Coordinates. Landscape Architecture and Regional Planning, 2(2), 61-66. https://doi.org/10.11648/j.larp.20170202.13
ACS Style
Sebahattin Bektas. Curvature of the Ellipsoid with Cartesian Coordinates. Landsc. Archit. Reg. Plan. 2017, 2(2), 61-66. doi: 10.11648/j.larp.20170202.13
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Download@article{10.11648/j.larp.20170202.13,
author = {Sebahattin Bektas},
title = {Curvature of the Ellipsoid with Cartesian Coordinates},
journal = {Landscape Architecture and Regional Planning},
volume = {2},
number = {2},
pages = {61-66},
doi = {10.11648/j.larp.20170202.13},
url = {https://doi.org/10.11648/j.larp.20170202.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.larp.20170202.13},
abstract = {This study aims to show how to obtain the curvature of the ellipsoid depending on azimuth angle. The curvature topic is quite popular at an interdisciplinary level. It can be to the friends of geometry, geodesy, satellite orbits in space, in studying all sorts of elliptical motions (e.g., planetary motions), curvature of surfaces and concerning eye-related radio-therapy treatment, for example the anterior surface of the cornea is often represented as ellipsoidal in form. On the calculation of the curvature, there is a famous Euler formula for rotating ellipsoid that everyone knows. Let θ be the angle, in the tangent plane, measured clockwise from the direction of minimum curvature κ1. Then the normal curvature κn (θ) in direction θ is given by κn (θ) = κ1 cos2θ + κ2 sin2θ = κ1 + (κ2 - κ1) cos2θ I wonder how can a formula for a triaxial ellipsoid? So we started to work. And we finally found the formula for the triaxial ellipsoid.},
year = {2017}
}
TY - JOUR T1 - Curvature of the Ellipsoid with Cartesian Coordinates AU - Sebahattin Bektas Y1 - 2017/03/04 PY - 2017 N1 - https://doi.org/10.11648/j.larp.20170202.13 DO - 10.11648/j.larp.20170202.13 T2 - Landscape Architecture and Regional Planning JF - Landscape Architecture and Regional Planning JO - Landscape Architecture and Regional Planning SP - 61 EP - 66 PB - Science Publishing Group SN - 2637-4374 UR - https://doi.org/10.11648/j.larp.20170202.13 AB - This study aims to show how to obtain the curvature of the ellipsoid depending on azimuth angle. The curvature topic is quite popular at an interdisciplinary level. It can be to the friends of geometry, geodesy, satellite orbits in space, in studying all sorts of elliptical motions (e.g., planetary motions), curvature of surfaces and concerning eye-related radio-therapy treatment, for example the anterior surface of the cornea is often represented as ellipsoidal in form. On the calculation of the curvature, there is a famous Euler formula for rotating ellipsoid that everyone knows. Let θ be the angle, in the tangent plane, measured clockwise from the direction of minimum curvature κ1. Then the normal curvature κn (θ) in direction θ is given by κn (θ) = κ1 cos2θ + κ2 sin2θ = κ1 + (κ2 - κ1) cos2θ I wonder how can a formula for a triaxial ellipsoid? So we started to work. And we finally found the formula for the triaxial ellipsoid. VL - 2 IS - 2 ER -
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