Abstract: As the second paper of a series on the content update of European and American classic mechanics textbooks for science majors, this manuscript expounds the motivation to reform classical mechanics teaching contents and explores the update of traditional teaching contents via the analysis on the latest editions of 3 textbooks. In the 1970s, the advances in algebraic structures, geometric descriptions and chaotic motions of classical mechanics received extensive attentions. Classical mechanics became a flourishing discipline. Therefore it was necessary to update the content of classic mechanics textbooks. One way to update textbooks was to integrate new materials in revised versions. Actually chaotic dynamics was introduced into the latest revisions of the three reprinted and widely used classical mechanics textbooks. However, algebraic structures of classical mechanics has only integrated into a textbook for advanced mechanics courses, while global differential geometry has not yet been incorporated into classic mechanics textbooks.