On the nonexistence of three-dimensional tube orbits around the intermediate axis in a triaxial galaxy model.

A specific triaxial model for a galaxy was previously investigated by numerical methods. In that investigation tube orbits around the major axis (X), as well as tube orbits around the minor axis (Z), had been found, but no tube orbit around the intermediate axis (Y) had been encountered. The present paper shows, again by numerical methods, that Y-tube orbits nearly certainly do not exist in the adopted model. Instead, a new family of 'shell orbits' has been found. The existence of X- and Z-tube orbits and the replacement of Y-tube orbits by shell orbits are made understandable by a numerical determination of the stability or instability, respectively, of the relevant two-dimensional closed resonance orbits in the three symmetry planes of the model.