is consistent with that for the traditional photometric classification in Sa, Sb, Sc. We conclude that $\sigma/V_{\rm C}$ is a good parameter to classify galaxy type, and we argue that such classification based on dynamics more closely mirrors the physical properties of the observed galaxies, compared to visual (photometric) classification. We also argue that dynamical classification is useful for samples where eye inspection is not reliable or impractical. We conclude that $\sigma/V_{\rm C}$ is a suitable parameter to characterise the hierarchical assembly history that determines the disk-to-bulge ratio, and to expand the TF relation into a three-dimensional manifold, defined by luminosity, circular velocity and $\sigma/V_{\rm C}$.'
title: 'The Fundamental Manifold of spiral galaxies: ordered versus random motions and the morphology dependence of the Tully-Fisher relation.'
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galaxies: formation galaxies: evolution galaxies: kinematics and dynamics galaxies: structure galaxies: fundamental parameters galaxies: spiral

Introduction
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Galaxy scaling relations highlight the regularities that characterise galaxy formation. Of particular interest is the physical connection between the dynamical state of a galaxy, determined by its assembly history, and the galaxy photometric properties, tracing its stellar populations and its star formation history. The main dynamical quantity in such an analysis is the galaxy total gravitational potential, 