The present report is concerned with the problem of particle phase space distributions for a charged particle beam. A new approach is presented. It provides the possibility to specify various coordinates in the phase space. The main attention has been focused on the case where motion integrals are taken as phase coordinates. Using such coordinates, one can obtain a lot of self-consistent distributions. Some distributions for a breathing beam are considered as examples: generalized Brillouin flow, generalized KV distribution, and others. Besides, this approach allows simple graphical representation of various self-consistent distributions.