The winds theory is based on PDEs whose unknown is the velocity vector field depending on time and spatial coordinates. The geometric dynamics is formulated using ODEs associated to a flow and a Riemannian metric, where the unknown is the velocity vector field depending on time. In this paper, we join these ideas showing that some geometric dynamics models generate winds. The second part of this paper is focused on the stability analysis of the considered models.
| Published in | American Journal of Science, Engineering and Technology (Volume 2, Issue 1) |
| DOI | 10.11648/j.ajset.20170201.13 |
| Page(s) | 15-19 |
| 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), 2024. Published by Science Publishing Group |
Flow, Metric, Geometric Dynamics, Wind, Stability
| [1] | R. Aris, Vectors, Tensors and the Basic Equations of Fluid Flow, Dover Publ. Inc., New York, 1989. |
| [2] | V. I. Arnold, The Hamiltonian nature of the Euler equations of rigid body dynamics and of ideal fluid, Uspehi Matem. Nauk., XXIV, 3, 147, pp. 225-246, 1969. |
| [3] | A. J. Chorin, J. E. Marsden, A Mathematical Introduction to Fluid Mechanics, Springer-Verlag, New York, 2000. |
| [4] | S. Comsa, G. Cosovici, M. Craciun, J. Cringanu, N. Dumitriu, P. Matei, I. Rosca, O. Stanasila, A. Toma, C. Udriste (coordinator), Variational Calculus (in romanian), StudIS Publishing House, Iasi, 2013. |
| [5] | D. Isvoranu, C. Udriste, Fluid flow versus Geometric Dynamics, BSG Proceedings, 13, pp. 70-82, 2006. |
| [6] | G. Schubert, C. C. Counselman, J. Hansen, S. S. Limaye, G. Pettengill, A. Seiff, I. I. Shapiro, V. E. Suomi, F. Taylor, L. Travis, R. Woo, R.E. Young, Dynamics, winds, circulation and turbulence in the atmosphere of venus, Space Science Reviews, 20, 4, pp. 357-387, 1977. |
| [7] | S. Treanta, On multi-time Hamilton-Jacobi theory via second order Lagrangians, U. P. B. Sci. Bull., Series A: Appl. Math. Phys., 76, 3, pp. 129-140, 2014. |
| [8] | C. Udriste, Geometric Dynamics, Mathematics and Its Applications, 513, Kluwer Academic Publishers, Dordrecht, Boston, London, 2000. |
| [9] | C. Udriste, Geodesic motion in a gyroscopic field of forces, Tensor, N. S., 66, 3, pp. 215-228, 2005. |
| [10] | C. Udriste, A. Udriste, From flows and metrics to dynamics and winds, Bull. Cal. Math. Soc., 98, 5, pp. 389-394, 2006. |
APA Style
Savin Treanţă, Elena-Laura Dudaş. (2017). Winds Generated by Flows and Riemannian Metrics. American Journal of Science, Engineering and Technology, 2(1), 15-19. https://doi.org/10.11648/j.ajset.20170201.13
ACS Style
Savin Treanţă; Elena-Laura Dudaş. Winds Generated by Flows and Riemannian Metrics. Am. J. Sci. Eng. Technol. 2017, 2(1), 15-19. doi: 10.11648/j.ajset.20170201.13
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.ajset.20170201.13,
author = {Savin Treanţă and Elena-Laura Dudaş},
title = {Winds Generated by Flows and Riemannian Metrics},
journal = {American Journal of Science, Engineering and Technology},
volume = {2},
number = {1},
pages = {15-19},
doi = {10.11648/j.ajset.20170201.13},
url = {https://doi.org/10.11648/j.ajset.20170201.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajset.20170201.13},
abstract = {The winds theory is based on PDEs whose unknown is the velocity vector field depending on time and spatial coordinates. The geometric dynamics is formulated using ODEs associated to a flow and a Riemannian metric, where the unknown is the velocity vector field depending on time. In this paper, we join these ideas showing that some geometric dynamics models generate winds. The second part of this paper is focused on the stability analysis of the considered models.},
year = {2017}
}
TY - JOUR T1 - Winds Generated by Flows and Riemannian Metrics AU - Savin Treanţă AU - Elena-Laura Dudaş Y1 - 2017/01/24 PY - 2017 N1 - https://doi.org/10.11648/j.ajset.20170201.13 DO - 10.11648/j.ajset.20170201.13 T2 - American Journal of Science, Engineering and Technology JF - American Journal of Science, Engineering and Technology JO - American Journal of Science, Engineering and Technology SP - 15 EP - 19 PB - Science Publishing Group SN - 2578-8353 UR - https://doi.org/10.11648/j.ajset.20170201.13 AB - The winds theory is based on PDEs whose unknown is the velocity vector field depending on time and spatial coordinates. The geometric dynamics is formulated using ODEs associated to a flow and a Riemannian metric, where the unknown is the velocity vector field depending on time. In this paper, we join these ideas showing that some geometric dynamics models generate winds. The second part of this paper is focused on the stability analysis of the considered models. VL - 2 IS - 1 ER -
Information
Email: