The authors of the new textbook Engineering Dynamics: A Comprehensive Introduction have written a short Primer to the notation used in their book. The notation differs from that used in the traditional suite of introductory texts (Meriam, Bedford & Fowler, Hibbeler, Beer & Johnson), but this more sophisticated notation is necessary because, as Kasdin explains, this textbook is more comprehensive than anything else currently available. Much of the material that requires this notation, such as multiple frames or three-dimensional rigid body rotation, are not covered in other textbooks.
Kasdin notes that the goal of the primer is threefold: “to show that the notation serves a specific purpose and has pedagogical value, to show that it is not as extensive and different as people think (i.e., it can be categorized into a small number of elements), and that we did not invent it, but rather followed common practice, adopting it from many sources, and merely tried to make it more consistent, systematic, and clear.”
He also emphasizes that there are other more complete and advanced books that have adopted some variation of the notation used in Engineering Dynamics, so there are precedents already in place for their decision to utilize this notation.
You can download the primer here.