We interpret simulations of secularly-evolving disc galaxies through orbit morphology. Using a new algorithm that measures the volume of orbits in real space using a tessellation, we rapidly isolate commensurate (resonant) orbits. We identify phase-space regions occupied by different orbital families. Compared to spectral methods, the tessellation algorithm can identify resonant orbits within a few dynamical periods, crucial for understanding an evolving galaxy model. The flexible methodology accepts arbitrary potentials, enabling detailed descriptions of the orbital families. We apply the machinery to four different potential models, including two barred models, and fully characterise the orbital membership. We identify key differences in the content of orbit families, emphasising the presence of orbit families indicative of the bar evolutionary state and the shape of the dark matter halo. We use the characterisation of orbits to investigate the shortcomings of analytic and self-consistent studies, comparing our findings to the evolutionary epochs in self-consistent barred galaxy simulations. Using insight from our orbit analysis, we present a new observational metric that uses spatial and kinematic information from integral field spectrometers that may reveal signatures of commensurabilities and allow for a differentiation between models.
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