Jacobi field strange condition. I am currently reading a textbook (Kuehnel) saying that if $V,W \in T_pM$ are such that $\langle V,W \rangle =0$ and $\|V\|=\|W\|=1,$ then 
$Y(t):=D \exp(tV)(tW)$ is a Jacobi field.
The thing is, I don't understand why this textbook has all these conditions on $V,W$?
Isn't it true that this also holds if we have any $V,W \in T_pM,$ cause all we should need is a variation of geodesics.
 A: Let me expand my comment into a proper answer.
The map $Y(t)$ is a Jacobi field along the geodesic $\gamma(t)=\exp(tV)$ for any choices of $V$ and $W$.
If you want to normalize your geodesics to have unit speed, then you want $\|V\|=1$ to make $Y$ into a Jacobi field along a geodesic.
A Jacobi field along the geodesic in direction $V$ that vanish at $p$ is always of the form $Y$ for some $W$ and different $W$s give different Jacobi fields.
Therefore you have a natural parametrization of these Jacobi fields.
Notice that $Y$ depends linearly on $W$.
Normalizing $\|W\|=1$ is purely a matter of convenience.
If you choose $W=V$, you get the parallel Jacobi field corresponding to a variation in the speed of the geodesic.
If you want to look at geodesics of unit speed only, this Jacobi field does not even correspond to a geodesic variation.
The normal Jacobi fields are most interesting and any Jacobi field is a sum of a parallel one and a normal one, so it makes sense to restrict attention to normal ones.
This corresponds to demanding $\langle V,W\rangle=0$.
