  We construct an explicit example of a smooth isotopy $\{\xi_t\}_{t \in
[0,1]}$ of volume- and orientation-preserving diffeomorphisms on $[0,1]^n$ ($n
\geq 3$) that has infinite total kinetic energy. This isotopy has no
self-cancellation and is supported on countably many disjoint tubular
neighbourhoods of homothetic copies of the isometrically embedded image of
$(M,g)$, a "topologically complicated" Riemannian manifold-with-boundary.
However, there exists another smooth isotopy that coincides with $\{\xi_t\}$ at
$t=0$ and $t=1$ but of finite total kinetic energy.
