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

提出了一种利用表面积分来计算两个非球形刚体之间的力、扭矩和势能的新技术。该方法相对较快，并且允许我们解决具有 12 个自由度的球体和椭球对的全刚性二体问题。我们通过两种无量纲测试场景演示了该方法，一种是发生翻滚运动，另一种是物体的运动类似于陀螺。我们还在小行星双星 (66391) 1999 KW4 上测试了该方法，其中两个组件都被建模为椭球体或椭球体。两种不同的形状模型对偏心距和半长轴的影响可以忽略不计，但对沿z轴的角速度影响较大-方向。在所有情况下，能量和总角动量都是守恒的，模拟精度保持在机器精度水平。