= Central axis of a momentum system
{title2=$\mathbf b=\mathbf P\times\mathbf L/|\mathbf P|^2+\lambda\mathbf P$}
For nonzero total <momentum> $\mathbf P$, translating the origin by $\mathbf b$ changes <angular momentum> to $\mathbf L-\mathbf b\times\mathbf P$. The displayed line of origins makes this vector parallel to $\mathbf P$, equal to $(\mathbf L\cdot\mathbf P)\mathbf P/|\mathbf P|^2$. The invariant $\mathbf L\cdot\mathbf P$ cannot be removed by translation; if it is zero, angular momentum vanishes on this line.
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