Three-integral models of globular clusters

A rotating lowered Maxwellian model for globular clusters with an anisotropic velocity distribution is presented. In constructing these models all three of E, J-square, and J(z) have been treated as integrals of the motion in constructing the distribution function. Because the rotation leads to a nonspherical potential, J-squared is in fact only an approximate integral, and the distribution function does not obey the collisionless Boltzmann equation. The errors introduced by not employing the true third integral I(3) are small. These models have been applied to the globular cluster M13 in an accompanying paper.