The generalized Reissner-type operator of three-dimensional micropolar mechanics of solids is presented, on the basis of which the generalized Reissner-type operator of three-dimensional micropolar mechanics of thin solids with one small size is obtained under the new parameterization of the domains of these bodies. From the last Reissner-type operator, in turn, the generalized Reissner-type variational principle of three-dimensional micropolar mechanics of thin solids with one small size is derived under the new parametrization of the domains of these bodies. It should be noted that the advantage of the new parameterization is that it is experimentally more accessible than other parameterizations (Nikabadze in Development of the method of orthogonal polynomials in the classical and micropolar mechanics of elastic thin bodies, MSU Publishing House, 2014; Contemp Math. Fundam Dir 55:3–194, 2015; J Math Sci 225:1, 2017). Further, applying the method of orthogonal polynomials (expansion of unknown quantities in series in terms of a system of orthogonal polynomials), from the generalized Reissner-type variational principle of three-dimensional micropolar mechanics of thin solids with one small size under the new parameterization of the domains of these bodies, the Reissner variational principle of micropolar mechanics of thin solids with one small size in the moments with respect to the system of Legendre polynomials is derived. In addition, the method is described for obtaining the variational principles of Lagrange and Castigliano of micropolar mechanics of thin solid with one small size under the new parametrization of the domains of these bodies in moments with respect to systems of the first and second kind Chebyshev polynomials. The paper is a continuation of the work “Nikabadze, Ulukhanyan, On some variational principles in the three-dimensional micropolar theories of solid”; therefore, before reading this paper, the authors invite the interested reader to familiarize themselves with the work (Nikabadze and Ulukhanyan in On some variational principles in the three-dimensional micropolar theories of solids, submitted).

提出了固体三维微极力学广义Reissner型算子，在此基础上，在新的域参数化下得到了一个小尺寸薄固体三维微极力学广义Reissner型算子这些机构中。从最后一个 Reissner 型算子出发，在这些物体域的新参数化下，又推导出了一个小尺寸薄固体三维微极力学的广义 Reissner 型变分原理。应该注意的是，新参数化的优点是它在实验上比其他参数化更容易获得（Nikabadze 在弹性薄体的经典和微极力学中正交多项式方法的发展，MSU 出版社，2014; 当代数学。Fundam Dir 55:3–194, 2015; J 数学科学 225:1, 2017)。进一步，应用正交多项式方法（未知量在正交多项式系统方面的级数展开），从新参数化下的小尺寸薄固体三维微极力学的广义Reissner型变分原理在这些物体的域中，导出了小尺寸薄固体微极力学关于勒让德多项式系统的Reissner变分原理。此外，描述了针对第一类和第二类切比雪夫多项式系统，在这些物体的域的新参数化下，获得小尺寸薄固体微极力学的拉格朗日和卡斯蒂利亚诺变分原理的方法。该论文是“Nikabadze，Ulukhanyan，关于固体三维微极理论中的一些变分原理”一书的延续；因此，在阅读本文之前，作者请感兴趣的读者熟悉这项工作（Nikabadze 和 Ulukhanyan 在 On some variables principle in the 3D micropolar Theories of solids, 已提交）。固体三维微极理论中的一些变分原理”；因此，在阅读本文之前，作者请感兴趣的读者熟悉这项工作（Nikabadze 和 Ulukhanyan 在 On some variables principle in the 3D micropolar Theories of solids, 已提交）。固体三维微极理论中的一些变分原理”；因此，在阅读本文之前，作者请感兴趣的读者熟悉这项工作（Nikabadze 和 Ulukhanyan 在 On some variables principle in the 3D micropolar theories of solids, 已提交）。