吉布斯及其向量理论

Gibbs and His Vector Theory

向量理论是19世纪后半叶数学和物理学领域取得的重要成就之一。文章在系统分析吉布斯的向量分析工作的基础上,考察了吉布斯对向量系统的重要贡献和其思想来源。四元数思想是吉布斯创立向量系统的基础,麦克斯韦对四元数批判性的使用给吉布斯创立向量系统以启迪,时代为吉布斯创立向量理论做好了准备。敏锐的洞察力和卓越的个人才识使得吉布斯迈出了最重要也是最关键的一步,创立了现代意义下的向量分析系统。在物理学和天文学等方面的成功应用使得向量分析系统得到迅速发展并广为流传。

The vector theory is one of the important achievements of the domain of mathematics and physics in the second half of the 19th century. Based upon systematically analyzing the work of Gibbs, this paper discusses J. W. Gibbs’ significant contributions to vector theory and the origin of his thoughts. The idea of quarternions is the base of vector theory which J. W. Gibbs created. Maxwell’s gentle criticism and discriminating employment of quarternions methods probably did not go unnoticed by J. W. Gibbs, so t...