Automatic Differentiation in Multibody Helicopter Simulation

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. We also provide ideas, how to include flexible bodies and closed-loop parts in the MBS. To emphasize the applicability of our approach, we provide simulation results for rigid MBS helicopter models.