Sane, S. P. and Dickinson, M. H. (2001). J. Exp. Biol.204, 2607–2626.

The correct form of equation (1) is:

1

and not

1

The only difference is that in the second term of the correct equation, there is only one (not two) dots above φ, signifying a single and not a double derivative of stroke position with respect to time.