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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[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.
