Red uction of nonlinear dynamic systems by phase space analysis
Abstract
We look directly into the phase space of experimental or numerical data to derive nonlinear equations of motion. Our example is the dynamics of viscous droplets. While the smallest useful dimension of phase space turns out to be three, we apply methods to visualize four, five, six dimensions and more. These methods are Poincare sections and condensation of variables. The resulting equations of motion are extremely simple but nevertheless realistic.
References
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[2] J .W.S. Rayleigh. On the capillary phenomena of jets. Proc. R. Soc. Lond., 29:71-97, 1879.
[3] H. Lamb. Hydrodynamics. 6th ed., pp. 473-475 and 639-641. Cambridge University Press, 1932.
[4] S. Chandrasekhar. Hydrodynamic and Hydromagnetic Stability. pp. 466-477. Oxford, Clarendon Press, 1961.
[5] J .A. Tsamopoulos and R.A. Brown. Nonlinear oscillations of inviscid drops and bubbles. J. Fluid Mech. , 127:519- 537, 1983.
[2] J .W.S. Rayleigh. On the capillary phenomena of jets. Proc. R. Soc. Lond., 29:71-97, 1879.
[3] H. Lamb. Hydrodynamics. 6th ed., pp. 473-475 and 639-641. Cambridge University Press, 1932.
[4] S. Chandrasekhar. Hydrodynamic and Hydromagnetic Stability. pp. 466-477. Oxford, Clarendon Press, 1961.
[5] J .A. Tsamopoulos and R.A. Brown. Nonlinear oscillations of inviscid drops and bubbles. J. Fluid Mech. , 127:519- 537, 1983.
Published
2023-09-01
Issue
pp. 39-48
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Becker, E., Brosa, U. ., & Kowalewski, T. A. (2023). Red uction of nonlinear dynamic systems by phase space analysis. Computer Assisted Methods in Engineering and Science, 1(1-2), 39-48. https://cames3.ippt.pan.pl/index.php/cames/article/view/1528
