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 motion a 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 algebras in the plane is used. If the same transformation is applied to the Lorenz system with any values of the parameters, then one obtains Euler equations of a rigid body about 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" the cross-section of which has a butterfly-shape. Thus Lorenz's butterfly has been transformed into a tornado. (C) 2003 American Institute of Physics.

Lorenz integrable system moves a` la Poinsot

NUCCI, Maria Clara
2003

Abstract

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 motion a 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 algebras in the plane is used. If the same transformation is applied to the Lorenz system with any values of the parameters, then one obtains Euler equations of a rigid body about 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" the cross-section of which has a butterfly-shape. Thus Lorenz's butterfly has been transformed into a tornado. (C) 2003 American Institute of Physics.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11570/3213783
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