We study the mechanisms and evolutionary phases of bar formation in n-body simulations of a stellar disc and dark matter halo system using harmonic basis function expansion analysis to characterize the dynamical mechanisms in bar evolution. We correlate orbit families with phases of bar evolution by using empirical orthogonal functions that act as a spatial filter and form the gravitational potential basis. In both models we find evidence for three phases in evolution with unique harmonic signatures. We recover known analytic results, such as bar slowdown owing to angular momentum transfer. We also find new dynamical mechanisms for bar evolution: a steady-state equilibrium configuration and harmonic interaction resulting in harmonic mode locking, both of which may be observable. Additionally, we find that ellipse fitting may severely overestimate measurements of bar length by a factor of two relative to the measurements based on orbits that comprise the true backbone supporting the bar feature. The bias will lead to overestimates of both bar mass and bar pattern speed, affecting inferences about the evolution of bars in the real universe, such as the fraction of bars with fast pattern speeds. We propose a direct observational technique to compute the radial extent of trapped orbits and determine a dynamical length for the bar.
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