三元复数的指数形式及相关性质探讨

The discussion of a compound exponential form and interrelated characteristics on a ternary complex

三元复数是作者新近提出的一种“超复数”.文中先将三元复数表记成简洁直观的复指数形式,在此基础上接着讨论了三元复数的基本性质,然后再制定复指数形式的三元复数旋转积的运算规则.指出使用旋转积的概念可用于表达矢量的旋转,旋转的结果是可以形成柱面、锥面、球面等复杂的空间回转曲面.此外三元复数还可作为描述物体复杂空间运动的数学工具.

A ternary complex is a ＂super＇ complex＂ offered by author recently. First,it can be expressed as a simple compound exponential form. Based on this,the elementary characteristics of a terrary complex are studied. Next, it is determined for the calculating rules of the rotating multiplication on a ternary complex Of the compound exponential form and as pointed out,it is able to express the rotation of a vector by means of the concept of the rotating multiplication. As the result of rotation the complicated spatial curved surfaces are formed which are the cylindrical, conic and spherical surfaces. A ternary complex is also considered as the mathematical tool of describing a spatial motion of an object.