  Multibody dynamics simulations have become widely used tools for vehicle
systems analysis and design. As this approach evolves, it becomes able to
provide additional information for various types of analyses. One very
important direction is the optimization of multibody systems. Sensitivity
analysis of multibody system dynamics is essential for design optimization.
Dynamic sensitivities, when needed, are often calculated by means of finite
differences. However, depending of the number of parameters involved, this
procedure can be computationally expensive. Moreover, in many cases the results
suffer from low accuracy when real perturbations are used. This paper develops
the adjoint sensitivity analysis of multibody systems in the context of penalty
formulations. The resulting sensitivities are applied to perform dynamical
optimization of a full vehicle system.
