Substitute
$$
\mathbf f=-\boldsymbol\gamma\mathbin{\cdot}\mathbf r_t
+\mathbf f^A
$$
into force balance. With $\boldsymbol\mu=\boldsymbol\gamma^{-1}$,
$$
\mathbf r_t
=\boldsymbol\mu\mathbin{\cdot}
(\partial_s\mathbf F+\mathbf f^A).
$$
Projection onto the local frame gives
$$
\boxed{
W=\mathbf t\mathbin{\cdot}\boldsymbol\mu
(\partial_s\mathbf F+\mathbf f^A),
\qquad
U=\mathbf n\mathbin{\cdot}\boldsymbol\mu
(\partial_s\mathbf F+\mathbf f^A)
}.
$$


Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 344 / 3 / c / ii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-344/3/c/ii/solution