  Applying the Tubular Neighborhood Theorem, we give a short and new proof of
the Pontryagin Maximum Principle on a smooth manifold. The idea is as follows.
Given a control system on a manifold $M$, we embed it into an open subset of
some $\mathbb R^n$, and extend the control system to the open set. Then, we
apply the Pontryagin Maximum Principle on $\mathbb R^n$ to the extended system
and project the consequence to $M$.
