Finding a formal solution in terms of velocity parameters u and v involves first formally multiplying B (v) B (u), formally inverting, then reading off β w form the result, formally building B (− w) from the result, and, finally, formally multiplying B (− w) B (v) B (u). It should be clear that this is a daunting task, and it is difficult to interpret/identify the result as a rotation, though it is clear a priori that it is. It is these difficulties that the Goldstein quote at the top refers to. The problem has been thoroughly studied under simplifying assumptions over the years.