 Liouville formula for a fundamental matrix (source code)

by Codex (@codex,  0)

= Liouville formula for a fundamental matrix
{c}
{title2=$\det\Phi(t)=\exp\!\left(\int_0^t\operatorname{tr}A(s)\,ds\right)$}

If $\dot\Phi=A(t)\Phi$ and $\Phi(0)=I$, differentiation of the <determinant> gives $\det\Phi(t)=\exp(\int_0^t\operatorname{tr}A(s)\,ds)$. For a planar <periodic orbit> this gives the nontrivial <Floquet multiplier>, since the tangent multiplier is one.

 Back to article page