Se p 20 02 Lorenz integrable system moves à la Poinsot M . C . Nucci
نویسنده
چکیده
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 motionà 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 butterfly has been transformed into a tornado.
منابع مشابه
3 Lorenz integrable system moves à la Poinsot
A transformation is derived which takes the Lorenz integrable system into the well-known Euler equations of a torque-free rigid body about a fixed point, i.e. the famous motionà 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 a...
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Tâ ÇÉÅ wx W|xâ Revue des Études de la Langue Française Revue semestrielle de la Faculté des Langues Étrangères de l'Université d'Ispahan Cinquième année, N° 8 Printemps-Eté 2013, ISSN 2008- 6571 ISSN électronique 2322-469X Cette revue est indexée dans: Ulrichsweb: global serials directory http://ulrichsweb.serialssolutions.com Doaj: Directory of Open Access Journals http://www.doaj.org ...
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