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Jacobi Differential Equation (Calculus of Variations)


\begin{displaymath}
{d\over dx} \Omega_{\eta'}-\Omega_\eta={d\over dx} (f_{y'y}\eta+f_{y'y}\eta')-(f_{yy}\eta+f_{yy'}\eta')=0,
\end{displaymath}

where

\begin{displaymath}
\Omega(x,\eta,\eta')\equiv {\textstyle{1\over 2}}(f_{yy}\eta^2+2f_{yy'}\eta\eta'+f_{y'y}\eta'^2).
\end{displaymath}

This equations arises in the Calculus of Variations.


References

Bliss, G. A. Calculus of Variations. Chicago, IL: Open Court, pp. 162-163, 1925.




© 1996-9 Eric W. Weisstein
1999-05-25