Model reduction for constrained mechanical systems via spectral submanifolds

The paper’s Appendix A–C derive exactly the same kinematic reformulation, constraint-stabilized ODE, and spectral correspondence as the model. The model reproduces the identities from the Maggi-type factorization, the Γ-projected dynamics, the first-order ODE form, and the linear spectrum split with n_c copies at −α and the remaining 2(n−n_c) finite DAE eigenvalues. One nuance: the paper claims B(z) is invertible as long as M is invertible, citing [39]; the model correctly notes a sufficient and standard assumption is M symmetric positive definite, because Γ^T M Γ can be singular for indefinite M on Null(G). This is a mild assumption clarification rather than a contradiction to the core results.