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Fixed End, Allowed to Pivot

In this simple case, we have

\begin{subequations}\begin{align}w(0,t)&= 0 &\Longrightarrow&& v(0,t) = 0\\ \fra...
...\partial x^{2}} &= 0 &\Longrightarrow&& m(0,t) = 0 \end{align}\end{subequations}

$ v(0,t)=0$ is ensured by terminating the parallel junction at $ i=0$ with a short-circuit, so that $ V_{J,0}$ is forced to zero. From Figure 5.4(a), we see that as a result (really by construction), we have $ V_{x^{+},0}^{+} = -V_{x^{+},0}^{-}$. The second boundary condition, $ m(0,t) = 0$ can be enforced in a similar manner by terminating the series junction at grid location zero with an open circuit.

Stefan Bilbao 2002-01-22