This work presents a computational strategy for efficiently computing the long-range pairwise forces acting between rigid-bodies. This force maybe be gravitational, electrostatic, or any force of the form 1/rs where s is any power. Although there is no mathematical limitation on s, the error bound is a function of the separation distance between the rigid-body and the evaluation point. Therefore, ... [Show full abstract] close range forces may incur a much larger amount of error.
This strategy uses multipole expansions, in a body-fixed basis, to model the charge distribution of a body. For rigid multi-body systems, this results in a time-invariant multipole expansion for each body when the multipole expansions are formed using the body-fixed basis. These expansions can then be rotated to match the orientation of the rigid-body based on the known state variables of the body. Additionally, there is no limitation on the size of the rotation. The potential due to the rigid-body with embedded sources can then be determined for all other bodies in the system. Notably, the charge distribution of the body may result in an overall neutrality with no ill effects. A simple numerical example where the potential due to a simple dipole is computed at some distance and orientation is presented that demonstrates that an overall neutral rigid-body and associated multipole expansions can undergo large rotations without having to reformulate the multipole expansions.