The time dependent Dalitz plot analysis of the B$^(0)-(d) \rightarrow\pi^+\pi^-\pi^0$ three body decay channel allows a measurement of the CP violation parameter alpha which is free from discrete ambiguities between 0 and pi. Moreover, such a method can be used as a way to extract independently the values of the main QCD parameters associated to the decay. In exchange, in concert with an accurate mastery of the involved phenomenology, the most essential experimental constraint consists in obtaining a sufficiently pure and extended signal events sample. The aim of this thesis is to study and quantify the feasibility of the alpha extraction through such an analysis in the LHCb dedicated experimental hadronic framework. Considering fully reconstructed simulated events, we have shown, on the one hand, that the specific reconstruction of neutral pions with large momentum is essential, and, on the other hand, that the control of the high background level can only be performed efficiently by using a multivariate approach. The second part of this work has consisted in modelling all the experimental listed dilutions as realistic as possible to evaluate the $\alpha$ expected sensitivity. Studying different theoretical scenarii, we obtain $\sigma_(alpha)^(stat)\leq $ 10 degrees by considering one nominal year of data taking associated to a 2 fb^(-1) integrated luminosity, what emphasizes the potential of LHCb to run physics involving neutral pions.