= Active bending beam for a swimming fish
{title2=$G_{xx}=m_bh_{tt}+\mathcal D(m\mathcal Dh)$}
An active swimming beam has a total internal <bending moment> $G$ containing passive elasticity and muscular actuation. Neglecting cross-sectional rotary inertia, slice <angular momentum> balance identifies the internal transverse force with $G_x$. Slice <linear momentum> balance then gives $G_{xx}=m_bh_{tt}-F_{\rm body}$. In <Lighthill elongated-body theory>, $F_{\rm body}=-\mathcal D(m\mathcal Dh)$, where $\mathcal D=\partial_t+U\partial_x$. The body and its hydrodynamic <added mass> therefore contribute with the same sign to the acceleration coefficient. The positive quantity $\mathcal D(m\mathcal Dh)$ is the reaction on the fluid.
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