2008A&A...477..133M

We developed a new method for the construction of orbits in the field of gravitational potential of a plane galactic disk. On the basis of three isolating integrals of motion, the three invariants of motion were found as combinations of the elements of a Keplerian ellipse. The equation of so-called ``blending ovals'' representing the fourth-degree convex algebraic curve convenient for constructing the whole orbit was found. As an example, the values of the integrals of motion for a globular cluster Pal5 traveling along an almost plane meridional orbit were defined from the observational data, which were used to construct the blending contours of the cluster and its orbit. We also found a condition of periodicity for a certain class of orbits.