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Work-conjugacy between rotation-dependent moments and finite rotations

机译:与旋转有关的力矩与有限旋转之间的共轭性

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In this paper we investigate the work-conjugacy between rotation-dependent moments and finite rotation measures. The methodology adopted consists of writing all the relevant quantities in terms of the rotation vector, using expressions that remain exact in the finite rotation range. Through this procedure, we show how (i) to identify workconjugate (rotation-dependent) moments and rotation measures, (ii) to derive a necessary condition for moment conservativeness and (iii) to obtain the general form of an isotropic conservative rotation-dependent moment. Several moment and finite rotation definitions that have been used in the past are investigated and, in particular, it is shown that the various existing definitions for the so-called semi-tangential moments are distinct in the finite rotation range and that not all of them are conservative. The tangent operator symmetry is discussed in the context of finite element analysis of conservative systems with rotational degrees of freedom, adopting either an additive or a multiplicative update. (C) 2003 Elsevier Science Ltd. All rights reserved. [References: 25]
机译:在本文中,我们研究了与旋转有关的力矩与有限旋转措施之间的共轭性。所采用的方法包括使用在有限旋转范围内保持精确的表达式,根据旋转矢量编写所有相关量。通过此过程,我们显示了如何(i)识别功共轭(与旋转有关的)力矩和旋转量度;(ii)得出矩保守性的必要条件;以及(iii)获得各向同性的与旋转有关的保守性的一般形式时刻。对过去使用的几种矩和有限旋转定义进行了研究,特别是表明,在所谓的半切向矩中,各种现有的定义在有限旋转范围内是不同的,并且并非全部是保守的。在具有旋转自由度的保守系统的有限元分析中,采用加法或乘法更新来讨论切线算子对称性。 (C)2003 Elsevier ScienceLtd。保留所有权利。 [参考:25]

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