  Following the Nambu mechanics framework we demonstrate that the
non-dissipative part of the Lorenz system can be generated by the intersection
of two quadratic surfaces that form a doublet under the group SL(2,R). All
manifolds are classified into four dinstict classes; parabolic, elliptical,
cylindrical and hyperbolic. The Lorenz attractor is localized by a specific
infinite set of one parameter family of these surfaces. The different classes
correspond to different physical systems. The Lorenz system is identified as a
charged rigid body in a uniform magnetic field with external torque and this
system is generalized to give new strange attractors.
