In this article we consider the problem to what extent the motion of gauge-charged matter that generates the gravitational field can be arbitrary, as well as what equations are superimposed on the gauge field due to conditions of compatibility of gravitational field equations. Considered problem is analyzed from the point of view symmetry of the theory with respect to the generalized gauge deformed groups without specification of Lagrangians. In particular it is shown, that the motion of uncharged particles along geodesics of Riemannian space is inherent in an extremely wide range of theories of gravity and is a consequence of the gauge translational invariance of these theories under the condition of fulfilling equations of gravitational field. In the cause of gauge-charged particles, the Lorentz force, generalized for gauge-charged matter, appears in equations of motion as a consequence of the gauge symmetry of the theory under the condition of fulfilling equations of gravitational and gauge fields. In addition, we found relationships of equations for some fields that follow from the assumption about fulfilling of equations for other fields. At the end of the article there is an Appendix, which briefly describes the main provisions and facts from the theory of generalized gauge deformed groups and presents the main ideas of a single group-theoretical interpretation of gauge fields of both external (space-time) and internal symmetry, which is an alternative to their geometric interpretation.

在本文中，我们考虑的问题是，在何种程度上，产生重力场的带荷电物质的运动可以是任意的，以及由于重力场方程的相容性条件，哪些方程式叠加在了规范磁场上。从理论的角度分析了所考虑的问题，该问题关于没有指定拉格朗日规的广义规范形变群。特别是表明，不带电的粒子沿黎曼空间测地线的运动是引力理论中极为广泛的固有现象，并且是在满足引力场方程的条件下这些理论的规范平移不变性的结果。在产生带正电荷的粒子的原因中，洛伦兹力（通常用于带正电荷的物质）在满足重力场和规范场方程的条件下，由于理论的规范对称性而在运动方程中出现。此外，我们发现某些领域的方程之间的关系遵循关于其他领域的方程满足的假设。本文末尾有一个附录，该附录简要描述了广义规范形变组理论的主要规定和事实，并提出了单个组的主要思想-外部（时空）规范场的理论解释和内部对称性，这是对其几何解释的一种替代。我们发现某些领域的方程之间的关系遵循了关于其他领域的方程满足的假设。本文末尾有一个附录，该附录简要描述了广义规范形变组理论的主要规定和事实，并提出了单个组的主要思想-外部（时空）规范场的理论解释和内部对称性，这是对其几何解释的一种替代。我们发现某些领域的方程之间的关系遵循了关于其他领域的方程满足的假设。本文末尾有一个附录，该附录简要描述了广义规范形变组理论的主要规定和事实，并提出了单个组的主要思想-外部（时空）规范场的理论解释和内部对称性，这是对其几何解释的一种替代。