A Symbolic Framework for Flexible Multibody Systems Applied to Horizontal Axis Wind Turbines

Emmanuel Branlard, Jens Geisler

Research output: Contribution to journalArticle


The article presents a symbolic framework that is used to obtain the linear and non-linear equations of motion of a multibody system including rigid and flexible bodies. Our approach is based on Kane's method and a nonlinear shape function representation for flexible bodies. The method yields compact symbolic equations of motion with implicit account of the constraints. The general and automatic framework facilitate the creation and manipulation of models with various levels of fidelity. The symbolic treatment provides analytical gradients and linearized equations of motion. The linear and non-linear equations can be exported to Python code or dedicated software. The application are multiple such as: time-domain simulation, stability analyses, frequency domain analyses, advanced controller design, state observers, digital twins, etc. In this paper, we describe the method we used to systematically generate the equations of motion of multibody systems. We apply the framework to generate illustrative onshore and offshore wind turbine models. We compare our results with OpenFAST simulations and discuss the advantages and limitations of the method. A Python implementation is provided as an opensource project.
Original languageAmerican English
Number of pages27
JournalWind Energy Science Discussions
StatePublished - 2021

NREL Publication Number

  • NREL/JA-5000-82458


  • equations of motion
  • multibody
  • symbolic
  • wind turbine


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