论SO（3）与P^3（R）同胚及其力学背景

On a homeomorphism of SO(3) with P￣3(R)and its meuchanics background

以微结构连续统的数学与力学特征描述为背景，从两个角度刻划刚子结构连续统的结构群ＳＯ（３）．从力学角度论证ＳＯ（３）与Ｐ３（Ｒ）同胚，并指出四元数理论与它的内在联系及力学意义．

wo characterizations of the structured group SO (3) of Cosserat Continua are given in this paper,with the background of mathematical and mechanical characteristics of continua with microstructure. From the view-point of mechanics,it is proved that SO(3) and P3 (R) are homeomorphic,and the relationship between P3 (R) and quaternion is pointed out. This work will be the role of a bridge for application of theory of fibre bundle to the study of the mechanical characteristics of new type materials.