We have developed a new method for determining the corotation radii ofdensity waves in disk galaxies, which makes use of the radial distribution ofan azimuthal phase shift between the potential and density wave patterns. Theapproach originated from improved theoretical understandings of the relationbetween the morphology and kinematics of galaxies, and on the dynamicalinteraction between density waves and the basic-state disk stars which resultsin the secular evolution of disk galaxies. In this paper, we present therationales behind the method, and the first application of it to severalrepresentative barred and grand-design spiral galaxies, using near-infraredimages to trace the mass distributions, as well as to calculate the potentialdistributions used in the phase shift calculations. We compare our results withthose from other existing methods for locating the corotations, and show thatthe new method both confirms the previously-established trends of bar-lengthdependence on galaxy morphological types, as well as provides new insights intothe possible extent of bars in disk galaxies. Application of the method to alarger sample and the preliminary analysis of which show that the phase shiftmethod is likely to be a generally-applicable, accurate, and essentiallymodel-independent method for determining the pattern speeds and corotationradii of single or nested density wave patterns in galaxies. Other implicationsof this work are: most of the nearby bright disk galaxies appear to possessquasi-stationary spiral modes; that these density wave modes and the associatedbasic state of the galactic disk slowly transform over time; and thatself-consistent N-particle systems contain physics not revealed by the passiveorbit analysis approaches.
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