  Normality equations describe Newtonian dynamical systems admitting normal
shift of hypersurfaces. These equations were first derived in Euclidean
geometry. Then very soon they were rederived in Riemannian and in Finslerian
geometry. Recently I have found that normality equations can be derived in
geometry given by classical and/or generalized Legendre transformation.
However, in this case they appear to be written in p-representation, i. e. in
terms of momentum covector and its components. The goal of present paper is to
transform normality equations back to v-representation, which is more natural
for Newtonian dynamical systems.
