Morphology of bar orbits.

I study the periodic orbits in a barred galaxy model potential, concentrating on the families that are relevant to the gas flow within the bar. This model has four free parameters- namely its central concentration and the axial ratio, quadrupole moment and pattern speed of its bar. It will be used in a companion paper to study the gas flow in and around the bar. Here I compare its properties to those of barred galaxies. I then describe a typical characteristic diagram and the different families of periodic orbits that constitute it. I discuss the existence and extent of the families x_2_ and x_3_ for realistic values of the free parameters of the model, and compare two different definitions of the inner Lindblad resonance in strong bar models. I then present the types of the 4/1 gap and the radii and stability of the Lagrangian points as a function of the same parameters.In the central parts of the galaxy the orbits of the x_1_ family are nearly circular. Their axial ratio increases with the size of the orbit, to reach a maximum value between 2 and 8, and then drops. The influence of the free parameters of the model on the position and value of the maximum is presented. Similar properties are obtained for the x_2_ and x_3_ families. The curvature of the x_1_ orbits at their apocentres also varies with the size of the orbit and with the main parameters of the model. Increasing the central concentration of the model or decreasing the bar pattern speed leads to more eccentric orbits with larger absolute values of the curvature at their apocentres.