可变形体的有限转动参数和回转磁效应

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The Finite Rotation Parameter of a Deformable Body and Gyromagnetic Effect

摘要: 本文的第一部份将Synge^[2]关于转动变换的推导用张量公式表达,进一步阐明作者在文[7]中所求得正交变换式的几何意义.文中并讨论转轴矢量的张量性质.文中后一部份应用拖带坐标系描述法讨论回转磁效应(Einstein-de Haas效应),建立一个求变形体中求磁化体力矩的简单公式.

Abstract: The derivation of Synge for the finite rotation formula in terms of Euler parameter is put into tensor form.Hence a further clarification of the geometric meaning of the orthogonal transformation obtained in the author's paper[7] is made. The tensor properties of rotation axis vector are also discussed. By means of the method of co-moving coordinate system established in[8],[9], we explain the gyromagnetic effect,and derive a simple formula for calculating body couple which is induced by magnetization.

[1]	Love.,A.E.H.,A treatise on the mathematical theory of elasticity,Dover,(1944),p.69.
[2]	Synge,J.L.,Classical dynamics,in“Handbuch der Physik”,Bd.ⅡI/1,10.
[3]	Kozik,T.J.,Finite rotations and associated displacement vector,J.Appl.Nech.,98(1976),698-699.
[4]	Koehler,T.R.and S.B.Trickey,Euler vectors and rotations about an arbitrary axis,Am.J.Phys.,46(6)(1978),650-651.
[5]	Wikes,J.M.,Rotations as solutions of a matrix differential equation,Am.J.Phys.46(6)(1978),685-687.
[6]	Beatty,M.F.,Vector analysis of finite rigid rotation,J.Appl.Mech.,99(1977),501-502.
[7]	陈至达,连续介质有限变形力学几何场论,力学学报,8(1979),107-117.中国矿院学报,1(1978),1-19.
[8]	陈至达,连续介质有限变形力学几何场论(广义弹性力学,岩石中的冲激波),中国矿院学报,2(1979),11-26.
[9]	陈至达,连续介质有限变形力学几何场论(弹性有限变形能量原理),清华大学学报,19,4(1979),44-57
[10]	陈至达,《有理力学》,中国矿院,北京,研究生部讲义,(1980).