<font face="Verdana, Arial" size="2">For example, from "step back, ride tiger" to lotus sweep, YZD and Yang Jun do not spin around with left foot suspended, while pivoting on the right foot as described in the book. Rather they turn around 135 deg, with both feet pivoted on the ground first before swinging the left foot in an arc to complete the turn.</font>
In my view, the problem may be that it is difficult to describe the subtleties of movement unambiguously. I could apply both of the above descriptions to Yang Zhenduo's form. The way I would describe the movement is as follows:
Begin pivoting on the ball of the left foot; and then, when the position becomes awkard, pivot on the ball of the right foot. The two pivots may slightly overlap. When the right foot becomes set after 135 degrees of turning, swing the left foot around with the intent of setting the heel down at the end of the turn. As the motion of the left leg makes the positioning of the right foot awkward, resume pivoting on the ball of the right foot and then set the heel of the left foot down. (During this motion, you are spinning with the left leg "suspended" and while pivoting on the right foot.) As you transfer weight to the left foot, pivot on the heel of the left foot to place the toes in the same position as Single Whip. At the same time as the left heel pivot, the right foot continues to pivot on the ball, but may finish slightly afterwards, since it is timed according to the weight shift.
<font face="Verdana, Arial" size="2">I also have a question that pertains to the book by Cheng Fu. How come there is no lifting of the arms in the opening posture?</font>
I vaguely recall one book that appears to leave out the Opening Form (Qi Shi). One explanation might be that the book does not show transitional postures. Since the Opening Form begins and ends with almost the same posture, a picture of the ending posture would look almost the same as the Preparation Form (Yubei Shi) and thus might be omitted.