Spinning equations of bi-metric type theories of gravity, the counterpart of the Papapetrou equations of motion are derived as well as their corresponding spinning deviation equations, by means of introducing different types of bi-metric theories. The influence of different curvatures based on different connections is illustrated. A specific Lagrangian function for each type theory is proposed, in order to derive the set of spinning motion and their corresponding spinning deviation equations.

中文翻译：

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双度量类型理论的纺纱和纺丝偏差方程

通过引入不同类型的双度量理论，得出了双度量重力理论的自旋方程，帕帕特鲁运动方程的对应物以及它们相应的旋转偏差方程。说明了基于不同连接的不同曲率的影响。提出了每种类型理论的特定拉格朗日函数，以推导旋转运动的集合及其对应的旋转偏差方程。