Nonlinear Sciences > Exactly Solvable and Integrable Systems
[Submitted on 22 Sep 2002 (v1), last revised 31 Aug 2003 (this version, v2)]
Title:Lorenz integrable system moves à la Poinsot
View PDFAbstract: A transformation is derived which takes Lorenz integrable system into the well-known Euler equations of a free-torque rigid body with a fixed point, i.e. the famous motion à la Poinsot. The proof is based on Lie group analysis applied to two third order ordinary differential equations admitting the same two-dimensional Lie symmetry algebra. Lie's classification of two-dimensional symmetry algebra in the plane is used. If the same transformation is applied to Lorenz system with any value of parameters, then one obtains Euler equations of a rigid body with a fixed point subjected to a torsion depending on time and angular velocity. The numerical solution of this system yields a three-dimensional picture which looks like a "tornado" whose cross-section has a butterfly-shape. Thus, Lorenz's {\em butterfly} has been transformed into a {\em tornado}.
Submission history
From: M. C. Nucci [view email][v1] Sun, 22 Sep 2002 02:14:53 UTC (362 KB)
[v2] Sun, 31 Aug 2003 21:15:28 UTC (22 KB)
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