  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.
