Results are reported from an amplitude analysis of the $B^+to D^+D^-K^+$ decay. The analysis is carried out using LHCb proton-proton collision data taken at $sqrt{s}=7,8,$ and $13$ TeV, corresponding to a total integrated luminosity of 9 fb$^{-1}$. In order to obtain a good description of the data, it is found to be necessary to include new spin-0 and spin-1 resonances in the $D^-K^+$ channel with masses around 2.9 GeV$/c^2$, and a new spin-0 charmonium resonance in proximity to the spin-2 $chi_{c2}(3930)$ state. The masses and widths of these resonances are determined, as are the relative contributions of all components in the amplitude model, which additionally include the vector charmonia $psi(3770)$, $psi(4040)$, $psi(4160)$ and $psi(4415)$ states and a nonresonant component.
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