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The polarimeter vector of the $\tau$ represents an optimal observable for themeasurement of the $\tau$ spin. In this paper we present an algorithm for thecomputation of the $\tau$ polarimeter vector for the decay channels $\tau^{-}\rightarrow \pi^{-}\pi^{+}\pi^{-}\nu_{\tau}$ and $\tau^{-} \rightarrow\pi^{-}\pi^{0}\pi^{0}\nu_{\tau}$. The algorithm is based on a model for thehadronic current in these decay channels, which was fitted to data recorded bythe CLEO experiment.

The polarimeter vector for $\tau \rightarrow 3 \pi\nu_{\tau}$ decays