  We study the geometric nature of the Jacobi equation. In particular we prove
that Jacobi vector fields (JVFs) along a solution of the Euler-Lagrange (EL)
equations are themselves solutions of the EL equations but considered on a
non-standard algebroid (different from the tangent bundle Lie algebroid). As a
consequence we obtain a simple non-computational proof of the relation between
the null subspace of the second variation of the action and the presence of
JVFs (and conjugate points) along an extremal. We work in the framework of
skew-symmetric algebroids.
