1. (adopted from Wiesel, Prob. 3, Ch. 2) One extremely confusing thing about meeting orbital mechanics for the first time is that almost anything can be expressed in either the geometric language of the orbital elements, or the dynamical language of energy, angular momentum, and so forth. Using the flight-path angle $\phi$, express the transverse and radial components of the velocity vector in terms of the energy $\mathcal{E}$, angular momentum $h$, the angle $\phi$ and the radius $r$.