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I want to solve

$$ \dot{\begin{pmatrix}C_1(t)\\C_2(t)\\C_3(t)\end{pmatrix}} = A\cdot\begin{pmatrix}C_1(t)\\C_2(t)\\C_3(t)\end{pmatrix}+\vec{b}(x) = \begin{pmatrix}0&a&b\\-a&0&c\\-b&-c&0\end{pmatrix}\cdot \begin{pmatrix}C_1(t)\\C_2(t)\\C_3(t)\end{pmatrix} + \begin{pmatrix}0\\V_{21}cos(wt)e^{w_{21}t}\\V_{31}cos(wt)e^{w_{31}t}\end{pmatrix} $$

however $A$ is not diagonalizeable. It has no eigenvectors and eigenvalues. Is there still a way to solve this ?

peter mafai
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    Rodrigues formula exponentiate 3 by 3 skew symmetric: https://math.stackexchange.com/questions/1747065/obtaining-the-rodrigues-formula https://math.stackexchange.com/questions/879351/matrix-exponential-of-a-skew-symmetric-matrix-without-series-expansion – Will Jagy Apr 18 '22 at 18:20
  • thanks. got it now. – peter mafai Apr 18 '22 at 19:41

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