Mutual potential between two rigid bodies with arbitrary shapes and mass distributions

Formulae to compute the mutual potential, force, and torque between two rigid bodies are given. These formulae are expressed in Cartesian coordinates using inertia integrals. They are valid for rigid bodies with arbitrary shapes and mass distributions. By using recursive relations, these formulae can be easily implemented on computers. Comparisons with previous studies show their superiority in computation speed. Using the algorithm as a tool, the planar problem of two ellipsoids is studied. Generally, potential truncated at the second order is good enough for a qualitative description of the mutual dynamics. However, for ellipsoids with very large non-spherical terms, higher order terms of the potential should be considered, at the cost of a higher computational cost. Explicit formulae of the potential truncated to the fourth order are given.