= Energy-neutral rotational nonlinearity
{title2=$x^TNx=0,\quad N^T=-N$}
A nonlinear term $f(|x|)Nx$ with real skew-symmetric <matrix> $N$ contributes zero to the derivative of the quadratic energy $|x|^2/2$. It changes orientation rather than magnitude directly. If a separate linear generator is a <non-normal matrix>, that reorientation can still alter later <transient growth>, so energy cancellation alone does not make the nonlinear evolution equivalent to the linear one.
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