Direct Differentiation and Adjoint Methods in Multiple Minimal Coordinates for Multibody System Sensitivity Analysis

Sensitivity analysis for multibody systems computes the gradient of a system's dynamic‐response cost functional with respect to design variables, enabling effective optimization of the system's response characteristics. Developing high‐fidelity, reliable, and computationally efficient sensitivity analysis methods is therefore of great importance. This paper proposes two novel approaches using multiple sets of minimal coordinates to achieve efficient sensitivity analysis for general multibody systems. Unlike methods based on Differential‐Algebraic Equations (DAEs), the proposed formulations express both the dynamic and adjoint equations as Ordinary Differential Equations (ODEs), ensuring strict satisfaction of position, velocity, and acceleration constraints throughout the computation. In contrast to methods that rely on a single predetermined set of minimal coordinates, this approach computes sensitivities globally without any risk of parameterization singularities. The approaches are validated on two planar multibody systems and compared against existing methods based on index‐1 DAE formulation and generalized coordinate partitioning. Simulation results show that the proposed methods are accurate, efficient, and globally valid.