  Based on $e^+e^-$ collision samples corresponding to an integrated luminosity
of 4.4 $\mbox{fb$^{-1}$}$ collected with the BESIII detector at center-of-mass
energies between $4.6\,\,\mathrm{GeV}$ and $4.7\,\,\mathrm{GeV}$, a partial
wave analysis of the charmed baryon hadronic decay
$\Lambda_c^+\to\Lambda\pi^+\pi^0$ is performed, and the decays
$\Lambda_c^+\to\Lambda\rho(770)^{+}$ and $\Lambda_c^+\to\Sigma(1385)\pi$ are
studied for the first time. Making use of the world-average branching fraction
$\mathcal{B}(\Lambda_c^+\to\Lambda\pi^+\pi^0)$, their branching fractions are
determined to be \begin{eqnarray*} \begin{aligned}
\mathcal{B}(\Lambda_c^+\to\Lambda\rho(770)^+)=&(4.06\pm0.30\pm0.35\pm0.23)\times10^{-2},\\
\mathcal{B}(\Lambda_c^+\to\Sigma(1385)^+\pi^0)=&(5.86\pm0.49\pm0.52\pm0.35)\times10^{-3},\\
\mathcal{B}(\Lambda_c^+\to\Sigma(1385)^0\pi^+)=&(6.47\pm0.59\pm0.66\pm0.38)\times10^{-3},\\
\end{aligned} \end{eqnarray*} where the first uncertainties are statistical,
the second are systematic, and the third are from the uncertainties of the
branching fractions $\mathcal{B}(\Lambda_c^+\to\Lambda\pi^+\pi^0)$ and
$\mathcal{B}(\Sigma(1385)\to\Lambda\pi)$. In addition, %according to amplitudes
determined from the partial wave analysis, the decay asymmetry parameters are
measured to be $\alpha_{\Lambda\rho(770)^+}=-0.763\pm0.053\pm0.045$,
$\alpha_{\Sigma(1385)^{+}\pi^0}=-0.917\pm0.069\pm0.056$, and
$\alpha_{\Sigma(1385)^{0}\pi^+}=-0.789\pm0.098\pm0.056$.

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