Low-order modeling of swimming using nonholonomic fin constraint

Traditional undulatory swimming models rely on complex fluid force representations with restrictive assumptions for fluid-structure-interaction (FSI) prediction. We developed a low-order, two-body model where the tail fin velocity is constrained to align with the fin angle via a nonholonomic (NH) constraint. In this approach, fluid forces on the fin arise from constraining the fin to move only in its alignment direction. The present implementation bypasses fin-normal force models (e.g., reactive model) but still requires a drag-force model to achieve steady swimming. Numerical simulations of the steady swimming of a matching system were conducted to validate the model. Excellent agreement was achieved for the body deformation and fluid force on the fin, although a fixed NH constraint does not apply exactly. Instead, an effective averaged NH constraint can be identified. The model performs robustly across a wide range of Reynolds and Strouhal numbers, as well as variations in tail-beat amplitude and frequency. Results show that the NH constraint approach efficiently captures essential swimming dynamics, offering an alternative to complex fluid force models in FSI problems involving fins. The model is limited due to an idealized geometry. Future work will implement additional body links for complex motion.