Consider a system consisting of a single mass with phase-space variables q, p= t, x, y,z, p0, px ,..

Consider a system consisting of a single
mass with phase-space variables q, p= t, x, y,z, p0, px , py , pz. Let the
generating function be G = nˆ · L where L = r × p is the angular momentum
vector and nˆ is an arbitrary, constant unit vector.

(a) Show that the differential changes of
position and momentum are δr = δa nˆ × r δp = δa nˆ × p
(18.120)

(b) Show that the generating function G =
nˆ · Lˆ generates a differential rotation of r and p by angle δa about
axis nˆ.