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L = m*r^2*(d[phi/dt))
d[phi] = du/sqrt(C(u) .
I = Int{u_<, u_> | du/sqrt(C(u)} .
Since I represents a net angle change (in radians) for the orbiting
particle when it goes from apapsis to periapsis we see that its
value is dimensionless, but the integrand 1/sqrt(C(u) has the
dimension of length and the differential du has the dimension of
inverse length. ....
I = Int{w_<, w_> | dw/sqrt(D(w)}