Direct differentiation of time integrators for multibody systems with absolute rotations

Gradient-based optimization methods require efficient algorithms to compute the sensitivities of the simulation results with respect to design parameters. Compared to finite difference schemes, the direct differentiation technique leads to a significant reduction in the computational cost of the sensitivities while keeping a good accuracy. In particular, this paper focuses on the optimization of multibody systems with large rotations. In this framework, two versions of the generalized-alpha time integration scheme are considered: the first one is based on a parameterized treatment of the rotations, whereas the second one is formulated in a geometric setting. We show that the sensitivity analysis is much simpler and computationally more efficient in the second case than in the first case. The performance of both algorithms is compared for a numerical example.