Lagrangian Dynamical Systems with Three Para-complex Structures

Ibrahim Yousif Ibrahim Abad Alrhman

doi:doi:10.11648/j.ijssam.20190404.11

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Lagrangian Dynamical Systems with Three Para-complex Structures

Ibrahim Yousif Ibrahim Abad Alrhman

Published in International Journal of Systems Science and Applied Mathematics (Volume 4, Issue 4)

Received: 21 March 2019 Accepted: 16 May 2019 Published: 17 January 2020

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Abstract

This paper aims to present Lagrangian Dynamical systems formalism for mechanical systems using Three Para- Complex Structures, which represent an interesting multidisciplinary field of research. As a result of this study, partial differential equations will be obtained for movement of objects in space and solutions of these equations. In this study, some geometrical, relativistic, mechanical, and physical results related to Three Para- Complex Structures mechanical systems broad applications in mathematical physics, geometrical optics, classical mechanics, analytical mechanics, mechanical systems, thermodynamics, geometric quantization and applied mathematics such as control theory.

Published in	International Journal of Systems Science and Applied Mathematics (Volume 4, Issue 4)
DOI	10.11648/j.ijssam.20190404.11
Page(s)	47-52
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), 2020. Published by Science Publishing Group

Keywords

Differential Geometry, Para-complex Structure, Lagrangian Dynamics

References

[1]	Mehmet Tekkoyun, On Para –Euler Lagrange and Para Hamiltonian Equations, physics letters A0 340 (2005) pp7-11.
[2]	Mehmet Mekkoyun and Murat Sari- Bi-Para Mechanical Equations on Lagrangian Distributions -arXivo: 0902. v1 [math. Ph] 8Jan 2009.
[3]	Mehmet Mekkoyun and Murat Sari Constrained para complex Mechanical Equations -arXivo: 0902-41210. v1 [math. DS] 24Feb 2009.
[4]	Oguzhan Celik and Zeki Kasap, Mechanical Equations with Two Almost Complex Structures on Symplectic Geometry, April 28, 2016.
[5]	Zeki Kasap and Mehmet Mekkoyun, Mechanical Equations on Bi-Para Conformal arXivo1209, 3101. V2 [math. GM] 22Sep 2010.
[6]	http//en.Wikipedia.org/wiki/almost complex structure.
[7]	Cristian Ida, Alexandru Ionescu and Adelina Manea, A note on para-holomorphic Riemannian Einstein manifolds, arXiv: 1507. 01114v2 [math. DG] 19 May 2016.
[8]	Z. Kasap and M. Tekkoyun, Mechanical Systems on Almost Para/ Pseudo Kähler. Weyl Manifolds, IJGMMP, Vol. 10, No. 5; 2013; 1-8.
[9]	R. Ye, Filling, By Holomorphic Curves In Symplectic 4 Man folds, Trans actions of The American Mathematical Society, Vol. 350, No. 1, 1998, pp. 213-250
[10]	New lander, A.; Nirenberg, L. (1957), "Complex analytic coordinates in almost complex manifolds", Annals of Mathematics. Second Series, 65 (3): 391–404, doi: 10. 2307/ 1970051, ISSN 0003-486X, JSTOR 1970051, MR 0088770.
[11]	Zeki KASAP, Hamilton Equations on a Contact 5 Manifolds, Elixir Adv. Math. 92 (2016) 38743-38748.
[12]	P. J. Higgins, K. Mackenzie: Algebraic constructions in the category of Lie algebraist, J. Algebra, 129 (1990), 194-230.
[13]	Z. Kasap, Weyl-Mechanical Systems on Tangent Manifolds of Constant W Sectional Curvature, Int. J. Geom. Methods Mod. Phys. Vol. 10, No. 10; 2013.
[14]	S. T. Lisi, Applications of Symplectic Geometry to Hamiltonian Mechanics, Department of Mathematics New York University, 2006.

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APA Style

Ibrahim Yousif Ibrahim Abad Alrhman. (2020). Lagrangian Dynamical Systems with Three Para-complex Structures. International Journal of Systems Science and Applied Mathematics, 4(4), 47-52. https://doi.org/10.11648/j.ijssam.20190404.11

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ACS Style

Ibrahim Yousif Ibrahim Abad Alrhman. Lagrangian Dynamical Systems with Three Para-complex Structures. Int. J. Syst. Sci. Appl. Math. 2020, 4(4), 47-52. doi: 10.11648/j.ijssam.20190404.11

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AMA Style

Ibrahim Yousif Ibrahim Abad Alrhman. Lagrangian Dynamical Systems with Three Para-complex Structures. Int J Syst Sci Appl Math. 2020;4(4):47-52. doi: 10.11648/j.ijssam.20190404.11

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@article{10.11648/j.ijssam.20190404.11,
  author = {Ibrahim Yousif Ibrahim Abad Alrhman},
  title = {Lagrangian Dynamical Systems with Three Para-complex Structures},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {4},
  number = {4},
  pages = {47-52},
  doi = {10.11648/j.ijssam.20190404.11},
  url = {https://doi.org/10.11648/j.ijssam.20190404.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20190404.11},
  abstract = {This paper aims to present Lagrangian Dynamical systems formalism for mechanical systems using Three Para- Complex Structures, which represent an interesting multidisciplinary field of research. As a result of this study, partial differential equations will be obtained for movement of objects in space and solutions of these equations. In this study, some geometrical, relativistic, mechanical, and physical results related to Three Para- Complex Structures mechanical systems broad applications in mathematical physics, geometrical optics, classical mechanics, analytical mechanics, mechanical systems, thermodynamics, geometric quantization and applied mathematics such as control theory.},
 year = {2020}
}

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TY  - JOUR
T1  - Lagrangian Dynamical Systems with Three Para-complex Structures
AU  - Ibrahim Yousif Ibrahim Abad Alrhman
Y1  - 2020/01/17
PY  - 2020
N1  - https://doi.org/10.11648/j.ijssam.20190404.11
DO  - 10.11648/j.ijssam.20190404.11
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 47
EP  - 52
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20190404.11
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Author Information

Ibrahim Yousif Ibrahim Abad Alrhman

Departmentof Mathematics, Faculty of Education, West Kordufan University, Alnhoud City, Sudan

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Ibrahim Yousif Ibrahim Abad Alrhman. (2020). Lagrangian Dynamical Systems with Three Para-complex Structures. International Journal of Systems Science and Applied Mathematics, 4(4), 47-52. https://doi.org/10.11648/j.ijssam.20190404.11

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ACS Style

Ibrahim Yousif Ibrahim Abad Alrhman. Lagrangian Dynamical Systems with Three Para-complex Structures. Int. J. Syst. Sci. Appl. Math. 2020, 4(4), 47-52. doi: 10.11648/j.ijssam.20190404.11

Copy | Download

AMA Style

Ibrahim Yousif Ibrahim Abad Alrhman. Lagrangian Dynamical Systems with Three Para-complex Structures. Int J Syst Sci Appl Math. 2020;4(4):47-52. doi: 10.11648/j.ijssam.20190404.11

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@article{10.11648/j.ijssam.20190404.11,
  author = {Ibrahim Yousif Ibrahim Abad Alrhman},
  title = {Lagrangian Dynamical Systems with Three Para-complex Structures},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {4},
  number = {4},
  pages = {47-52},
  doi = {10.11648/j.ijssam.20190404.11},
  url = {https://doi.org/10.11648/j.ijssam.20190404.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20190404.11},
  abstract = {This paper aims to present Lagrangian Dynamical systems formalism for mechanical systems using Three Para- Complex Structures, which represent an interesting multidisciplinary field of research. As a result of this study, partial differential equations will be obtained for movement of objects in space and solutions of these equations. In this study, some geometrical, relativistic, mechanical, and physical results related to Three Para- Complex Structures mechanical systems broad applications in mathematical physics, geometrical optics, classical mechanics, analytical mechanics, mechanical systems, thermodynamics, geometric quantization and applied mathematics such as control theory.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Lagrangian Dynamical Systems with Three Para-complex Structures
AU  - Ibrahim Yousif Ibrahim Abad Alrhman
Y1  - 2020/01/17
PY  - 2020
N1  - https://doi.org/10.11648/j.ijssam.20190404.11
DO  - 10.11648/j.ijssam.20190404.11
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 47
EP  - 52
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20190404.11
AB  - This paper aims to present Lagrangian Dynamical systems formalism for mechanical systems using Three Para- Complex Structures, which represent an interesting multidisciplinary field of research. As a result of this study, partial differential equations will be obtained for movement of objects in space and solutions of these equations. In this study, some geometrical, relativistic, mechanical, and physical results related to Three Para- Complex Structures mechanical systems broad applications in mathematical physics, geometrical optics, classical mechanics, analytical mechanics, mechanical systems, thermodynamics, geometric quantization and applied mathematics such as control theory.
VL  - 4
IS  - 4
ER  -

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