### Finding Energy of the Slant Helix Strip by Using Classic Energy Methods on Joachimsthal Theorem

Received: 15 February 2017     Accepted: 16 February 2017     Published: 6 March 2017
Abstract

There are two forms of mechanical energy-potential energy and kinetic energy in physics. Potential energy Ep is stored energy of position. The amount of kinetic energy Ek possesed by a moving object is depent upon mass and speed. The total mechanical energy possesed by an object is the sum of its kinetic and potential energies. Now we calculate the mathematical physic on Joachimsthal Theorem. In this paper, we find the eneryg of two curves on different surfaces and slant helix strips by using classic energy formulaes in Euclidean Space E3.

Keywords

Curve-Surface Pair (Strip), Curvature, Energy, Classic Energy Formulaes, Joachimsthal Theorem

References
 [1] Beardon, A. The Geometry Discrete Groups Springer-Verlag, Berlin, 1983, 9-81p. [2] Ertem Kaya, F., Yayli, Y., Hacisalihoglu, H. H. Harmonic Curvature of a Strip in E3, Communications de la faculté des Sciences De Université d. Ankara Serie A1, Tome 59, Number 2, 2010, Pages 37-51. [3] Ertem Kaya, F. Harmonic curvature of the curve-surface pair under Möbius Transformation, International Journal of Physical Sciences, Vol. 8 (21), 2013, pp. 1133-1142. [4] Ertem Kaya F., Yayli Y., Hacisalihoglu H. H., The Conical Helix Strip in E3, Int. J. Pure Appl. Math. Volume 66, No (2), Pages 145-156, 2011. [5] Ertem Kaya F.,. Terquem Theorem with the Spherical helix Strip., Pure and Applied Mathematics Journal, Applications of Geometry, Vol. 4, Issue Number 1-2, January 2015, DOI: 10.11648/j.pamj.s.2015040102.12 [6] ON INVOLUTE AND EVOLUTE OF THE CURVE AND CURVE-SURFACE PAIR IN EUCLIDEAN 3-SPACE., Pure and Applied Mathematics Journal, Applications of Geometry, Vol. 4, Issue Number 1-2, January 2015, DOI: 10.11648/j.pamj.s.2015040102.11. [7] Gang Hu, Xinqiang Qin, Xiaomin Ji, Guo Wei, Suxia Zhang, The construction of B-spline curves and itsapplication to rotational surfaces, Applied Mathematics and Computation 266 (2015) 194.211. [8] Gluck, H. Higher Curvatures of Curves in Eucliden Space, Amer. Math. Montly. 73, 1966, pp: 699-704. [9] Hacisalihoglu, H. H. On The Relations Between The Higher Curvatures Of A Curve and A Strip., Communications de la faculté des Sciences De Université d. Ankara Serie A1, (1982), Tome 31. [10] Keles, S. Joachimsthal Theorems for Manifolds [PhD] Firat University, 1982, pp. 15-17. [11] http://tr.wikipedia.org/wiki/Enerji. [12] Horn, B. K. P., The Curve of Least Energy, Massachusetts Institute of Technology, ACM Transactions on Mathematical Software, Vol. 9, No. 4, December 1983, Pages 441-460. [13] http://www.physicsclassroom.com/calcpad/energy. [14] Yaşar Yavuz, A., Ekmekci, F. N., Yayli, Yusuf, On the Gaussian And Mean Curvatures Parallel Hypercurfaces in E1n+1, British Journal of Mathematics & Computer Science, 4 (5), p: 590-596, 2014. [15] Ayşe Yavuz, F. Nejat Ekmekci, Constant Curvatures of Parallel Hypersurfaces in E1n+1, Lorentz Space, Pure and Applied Mathematics Journal. Special Issue: Applications of Geometry. Vol. 4, No. 1-2, 2015, pp. 24-27. doi: 10.11648/j.pamj.s.2015040102.16.
• APA Style

Filiz Ertem Kaya. (2017). Finding Energy of the Slant Helix Strip by Using Classic Energy Methods on Joachimsthal Theorem. Pure and Applied Mathematics Journal, 6(3-1), 1-5. https://doi.org/10.11648/j.pamj.s.2017060301.11

ACS Style

Filiz Ertem Kaya. Finding Energy of the Slant Helix Strip by Using Classic Energy Methods on Joachimsthal Theorem. Pure Appl. Math. J. 2017, 6(3-1), 1-5. doi: 10.11648/j.pamj.s.2017060301.11

AMA Style

Filiz Ertem Kaya. Finding Energy of the Slant Helix Strip by Using Classic Energy Methods on Joachimsthal Theorem. Pure Appl Math J. 2017;6(3-1):1-5. doi: 10.11648/j.pamj.s.2017060301.11

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author = {Filiz Ertem Kaya},
title = {Finding Energy of the Slant Helix Strip by Using Classic Energy Methods on Joachimsthal Theorem},
journal = {Pure and Applied Mathematics Journal},
volume = {6},
number = {3-1},
pages = {1-5},
doi = {10.11648/j.pamj.s.2017060301.11},
url = {https://doi.org/10.11648/j.pamj.s.2017060301.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2017060301.11},
abstract = {There are two forms of mechanical energy-potential energy and kinetic energy in physics. Potential energy Ep is stored energy of position. The amount of kinetic energy Ek possesed by a moving object is depent upon mass and speed. The total mechanical energy possesed by an object is the sum of its kinetic and potential energies. Now we calculate the mathematical physic on Joachimsthal Theorem. In this paper, we find the eneryg of two curves on different surfaces and slant helix strips by using classic energy formulaes in Euclidean Space E3.},
year = {2017}
}
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AB  - There are two forms of mechanical energy-potential energy and kinetic energy in physics. Potential energy Ep is stored energy of position. The amount of kinetic energy Ek possesed by a moving object is depent upon mass and speed. The total mechanical energy possesed by an object is the sum of its kinetic and potential energies. Now we calculate the mathematical physic on Joachimsthal Theorem. In this paper, we find the eneryg of two curves on different surfaces and slant helix strips by using classic energy formulaes in Euclidean Space E3.
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Author Information
• Department of Mathematics, Faculty of Science and Arts, University of Omer Halisdemir Campus, Nigde, Turkey

• Sections