2210.16965
Development of an Efficient Formulation for Volterra’s Equations of Motion for Multibody Dynamical Systems
Mohammad Hussein Yoosefian Nooshabadi, Hossein Nejat Pishkenari
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper derives: (i) the dynamical constraints M' q̇ + N' = 0 from d/dt(∂L/∂q̇_I)=0 under the definition of ignorable coordinates (Eq. 25) ; (ii) the reduced Volterra equations for p−s independent quasi-velocities u_NI (Eq. 41) ; (iii) the affine velocity map q̇ = W_NI u_NI + X_NI obtained by stacking quasi-velocity definitions with kinematic and dynamical constraints (Eqs. 42–44) ; (iv) the kinetic energy in u_NI-coordinates and d/dt(∂T/∂u_NI) = M_NI u̇_NI + A_NI (Eqs. 46–52) ; (v) the matrix ODE M_NI u̇_NI = L_NI = U_NI + F_NI − A_NI and state-space form (Eqs. 64–67) . The candidate solution reproduces exactly these steps (Tasks A–C), including the same constructions W_NI, X_NI, M_NI, A_NI, and the minimality argument (invertibility of the stacked matrix), so both are correct and essentially the same approach.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The work presents a coherent and efficient reduction of Volterra’s equations for systems with ignorable coordinates by embedding dynamical constraints into the formulation. The derivations are consistent with classical mechanics and are supported by clear matrix/state-space representations and numerical examples. Minor revisions are advisable to tighten the mathematical assumptions (rank conditions, ideality, smoothness) and to clarify the independence of the stacked constraints and quasi-velocity definitions.