Abstract
In a first approximation, helicopters can be modeled by open-loop multibody systems (MBS). For this type of MBS the joints’ degrees of freedom provide a globally valid set of minimal states. We derive the equations of motion in these minimal coordinates and observe that one has to compute Jacobian matrices of the bodies’ kinematics with respect to the minimal states. Classically, these Jacobians are derived analytically from a complicated composition of coordinate transformations. In this paper, we will present an alternative approach, where the arising Jacobians are computed by automatic differentiation (AD). This makes the implementation of a simulation code for open-loop MBS more efficient, less error-prone, and easier to extend. To emphasize the applicability of our approach, we provide simulation results for rigid MBS helicopter models.
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Bhalerao, K.D., Poursina, M., Anderson, K.S.: An efficient direct differentiation approach for sensitivity analysis of flexible multibody systems. Multibody Syst. Dyn. 23, 121–140 (2010)
Bischof, C.H.: On the automatic differentiation of computer programs and an application to multibody systems. In: Bestle, D., Schielen, W. (eds.) IUTAM Symposium on Optimization of Mechanical Systems, pp. 41–48. Springer (1996)
Callejo, A., Dopico, D.: Direct sensitivity analysis of multibody systems: a vehicle dynamics benchmark. J. Comput. Nonlinear Dynam. 14, 021004 (2019)
Callejo, A., Narayanan, S.H.K., Garcia de Jalon, J., Norris, B.: Performance of automatic differentiation tools in the dynamic simulation of multibody systems. Adv. Eng. Software 73, 35–44 (2014)
Eberhard, P., Bischof, C.: Automatic differentiation of numerical integration algorithms. Math. Comp. 68, 717–731 (1999)
Griffith, D.T., Turner, J.D., Junkins, J.L.: Some applications of automatic differentiation to rigid, flexible, and constrained multibody dynamics. In: Proceedings of IDETC/CIE 2005. ASME (2005)
Guennebaud, G., Jacob, B., et al.: Eigen v3 (2010). http://eigen.tuxfamily.org
Hairer, E., Lubich, C., Wanner, G.: Geometric Numerical Integration, 2nd edn. Springer, Heidelberg (2006)
Johnson, W.: Rotorcraft Aeromechanics. Cambridge Aerospace Series. Cambridge University Press, Cambridge (2013)
Naumann, U.: The Art of Differentiating Computer Programs. SIAM, Philadelphia (2012)
Schwertassek, R., Wallrapp, O.: Dynamik flexibler Mehrkörpersysteme. Vieweg (1999)
Serban, R., Haug, E.J.: Kinematic and kinetic derivatives in multibody systems. Mech. Struct. Mach. 26, 145–173 (1998)
Simeon, B.: Computational Flexible Multibody Dynamics. Springer, Heidelberg (2013)
van der Wall, B.G.: Grundlagen der Hubschrauber-Aerodynamik. Springer Vieweg (2015)
van der Wall, B.G.: Grundlagen der Dynamik von Hubschrauber-Rotoren. Springer Vieweg (2018)
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Kontak, M., Röhrig-Zöllner, M., Hofmann, J., Weiß, F. (2020). Automatic Differentiation in Multibody Helicopter Simulation. In: Kecskeméthy, A., Geu Flores, F. (eds) Multibody Dynamics 2019. ECCOMAS 2019. Computational Methods in Applied Sciences, vol 53. Springer, Cham. https://doi.org/10.1007/978-3-030-23132-3_64
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DOI: https://doi.org/10.1007/978-3-030-23132-3_64
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