= Stress characteristics for an anisotropic yield curve
{title2=$d(\sigma-l)=0\ \text{on }\alpha,\qquad d(\sigma+l)=0\ \text{on }\beta$}
Parameterize a fixed <yield surface> by stress-space <arc length> $l$ with $\xi_{,l}=-\cos2\phi$ and $\tau_{,l}=-\sin2\phi$. For mean normal stress $\sigma$, <force balance> gives $\nabla\sigma=M\nabla l$, where $M=\begin{pmatrix}\cos2\phi&\sin2\phi\\\sin2\phi&-\cos2\phi\end{pmatrix}$. Its eigenvectors along angles $\phi$ and $\phi+\pi/2$ have <eigenvalues> $+1$ and $-1$, proving the displayed <slip line> invariants.
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