I don't understand it myself, maybe somebody else has a good explanation. Or maybe not; the opening quote of Sussman and Wisdom is:
>“In almost all textbooks, even the best, this principle is presented so that it is impossible to understand.” (K. Jacobi, Lectures on Dynamics, 1842-1843). I have not chosen to break with tradition.
>V. I. Arnold, Mathematical Methods of Classical Mechanics , footnote, p. 246