Discrete adjoint variable method for the sensitivity analysis of ALI3-P formulations

The sensitivity analysis of the dynamics of multibody systems is a topic that has been attracting the attention of several researchers for years, particularly due to its value in optimal control and design problems. Depending on the dynamic formulation and the sensitivity method considered, different sets of sensitivity systems of equations would be reached involving diverse complexity levels. In this work, the analytical sensitivity analysis of the augmented Lagrangian index-3 formulation with velocity and acceleration projections (ALI3-P) is developed using the discrete adjoint variable method, considering a Newmark’s family integrator for the numerical integration of the forward dynamics, adjoint sensitivity and gradient equations, and a penalty formulation for the initial acceleration problem. The accuracy and efficiency of the new sensitivity formulation are tested in a five-bar mechanism benchmark problem and in the multibody model of a real-life four-wheeled vehicle. The method has been implemented in the MBSLIM multibody library as two general sensitivity formulations over the already existing global and topological forward dynamics formulations in natural and joint coordinates respectively.