Spectral stellar dynamics

Studies are conducted of orbits in a class of nonrotating bar-like potentials in which essentially all orbits appear to be regular in the sense that they are confined in phase space by a nonclassical integral in addition to the energy. The spectra of these orbits are decomposed into a series of pure sinusoidal components, or lines. The production and analysis of spectra is discussed along with the spectra of typical orbits, taking into account orbits in axisymmetric potentials and in nonaxisymmetric potentials. Questions regarding the physical interpretation of spectra are explored, giving attention to Floquet's theorem and aspects of precession and libration. The interpretation of loop orbits as precessing ellipses and of box orbits as librating axial orbits leads to a simple picture of the nature of the important transition from loop to box orbits.