The general three-body problem is investigated with the addition of a fixed external force applied to one of the masses. It is firstly demonstrated that the centre-of-mass of the three-body system accelerates. Then, it is demonstrated that only a single, unstable, collinear equilibrium solution exits in the accelerating frame. While unstable, it is also demonstrated that this single equilibrium configuration is in principle controllable using additional control accelerations distributed between the masses. Potential applications of such an accelerated collinear equilibrium configuration are discussed for the active manoeuvring of chains of small asteroids for space resource utilisation.

中文翻译：

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加速三体问题中的平衡

通过向其中一个质量施加固定外力来研究一般的三体问题。首先证明了三体系统质心加速。然后，证明了加速框架中仅存在单一的、不稳定的共线平衡解。虽然不稳定，但也证明了这种单一平衡配置原则上可以使用分布在质量之间的附加控制加速度进行控制。讨论了这种加速共线平衡配置的潜在应用，用于主动操纵小行星链以利用空间资源。