Extended two-body problem for rotating rigid bodies

A new technique that utilizes surface integrals to find the force, torque and potential energy between two non-spherical, rigid bodies is presented. The method relatively fast, allows us solve full two-body problem for pairs of spheroids ellipsoids with 12 degrees freedom. We demonstrate dimensionless test scenarios, one where tumbling motion develops, resemble spinning tops. also on asteroid binary (66391) 1999 KW4, both components are modelled either as or ellipsoids. different shape models have negligible effects eccentricity semi-major axis, but a larger impact angular velocity along $z$-direction. In all cases, total momentum conserved, simulation accuracy kept at machine level.