After reviewing carefully, the paper titled “A symbolic framework for flexible multibody system applied to horizontal axis wind turbines”, I have arrived to the following conclusion:

Without underestimating the programming effort and authors' particular motivation, I strongly think that the proposed work does not contribute in any form to the current state of the art in flexible multibody dynamics applied to horizontal axis wind turbines. The methods proposed are not new. Moreover, the assumption made on the elastic deformation of the flexible bodies is quite limited and thus, it requires amendments such us the inclusion of softening/stiffening terms. There are some formulations available in the literature, for instance the geometrically exact beam developed during the eighties and nineties, that can be already implemented in “pseudo” real time and are by far superior to the approach proposed by the authors. Therefore, based on my assessment I regrettably cannot recommend the paper for publication, even after major changes.

As the title states, this paper presents a symbolic framework for flexible multibody systems applied to HAWTs.  Overall, the approach is clearly presented and shows excellent agreement to OpenFAST.  Moreover, in addition to the paper, a companion open-source Python implementation is provided so readers can repeat the analysis and apply the approach to general systems.  In contrast to the other reviewers comments, I would strongly encourage publication of this article.  Novel items include a (1) clear and concise presentation of flexible multibody dynamics expressed in Kane's formulation, applicable to both nonlinear and linearized systems, in symbolic form and (2) an open-source Python implementation based on SymPy and PyDy.  While the formulation will not replace widely used structural dynamics software for HAWTs such as OpenFAST, Bladed, HAWC2, and FLEX5, that is not the intent, as stated.  While the approach could be used to simplify or enhance the ElastoDyn module of OpenFAST, more important applications, as stated, include frequency-domain analysis important in preliminary design, stability analysis, controls design, physics-based digital twins, etc.  The approach does account for centrifugal stiffenning and gravitational destiffenning.



Please a find a few specific comments below:

Section 2: The ElastoDyn module of OpenFAST uses the concept of "partial loads", which is extension of the "partial velocity" approach used by Kane's method.  Partial loads simplify the formulation of the equations of motion into terms that are useful for load output calculations once the equations of motion are solved.  I don't see this concept mention, but perhaps it would be an interesting extension of the described approach, if possible?

Page 1, Line 4: Change "facilite" to "facilitates".

Page 1, Line 6: Change "application" to "applications".

Page 3, Line 79: "masscenter" should be two words. 

Page 4, Line 93: Change "is" to "are".

Page 5, Line 129: Change "reminder" to "remainder".

Page 6, Line 141: It would be useful to mention the contribution of the inertia term (M*qdd) on the stiffness matrix, which can impact the linearized solution if the model is not in steady state, where otherwise qdd = 0).

Page 6, Line 158: "Shape functions of any order" are mentioned.  Is this referring to shape functions expressed as polynomials?  Are other forms of shape functions permitted in the Python implementation?

Page 20, Line 467: Change "of" to "or".

Page 22, Line 508: Add "be" after "to".