Rigid Body Dynamics in Ambient Fluids

TL;DR

This work tackles real-time rigid-body dynamics in ambient fluids without full fluid simulations by coupling a surface-based added-mass model with a flow-separation driven dynamic-pressure force. By solving a potential-flow Neumann problem and introducing a separation-angle parameter $\alpha$, the authors compute dynamic pressures and skin-friction forces from surface slip velocities, enabling accurate replication of complex phenomena such as fluttering, tumbling, chaotic descent, and the Magnus effect. The approach yields a 6×6 inertia tensor that blends body and fluid inertia, with preprocessing via boundary-integral equations and per-step force evaluations that fit into standard RBD solvers. The framework is demonstrated across diverse scenarios (falling plates, football golf-ball curl, basketball drift, underwater motion, balloons, copter) and shown to outperform baselines that rely on artificial damping or full CFD, offering a practical, scalable tool for graphics and engineering applications.

Abstract

We present a novel framework for rigid body dynamics in ambient media, such as air or water, enabling accurate motion prediction of objects without requiring computational fluid dynamics simulations. Our method computes the added mass of the fluid and replaces heuristic models for shape-dependent lift and drag with a generalized estimate of flow separation and dynamic pressure. Our method is the first within the rigid body dynamics context to reproduce the full range of falling plate behaviors: fluttering, tumbling, chaotic and steady modes, as well as phenomena such as the Magnus effect and the flight dynamics of an American football (tight spiral pass paradox). The resulting algorithm is simple to implement, robust, does not rely on specialized integrators and incorporates seamlessly into existing physics engines for real-time simulation.

Figures (19)

• Figure 1: Overview of our algorithm. Given a watertight triangulated surface mesh and physical parameters as input, we first perform preprocessing to compute quantities invariant during runtime. In the simulation loop, our proposed forces are computed and then integrated in the standard rigid-body dynamics way.
• Figure 2: State variables of a rigid body dynamics system. In the body frame (left), angular velocity $\mathbf{w}$ and linear velocity $\mathbf{v}$ define the motion, along with applied torque $\mathbf{\tau}$ and force $\mathbf{f}_{}$. The world frame (right) tracks the body's position $\mathbf{y}$ and orientation $\mathbf{q} \in \mathbb{S}^3$. Frame transformations are performed via quaternion conjugation, e.g., $\dot{\mathbf{y}} = \mathbf{q} \, \mathbf{v} \, \mathbf{q}^{-1}$.
• Figure 3: Potential flow fields $\mathbf{u} = \nabla \phi$ induced by different components of rigid body motion $(\mathbf{w}, \mathbf{v})$ for an elliptical body (2D-slice view). (a) Horizontal translation induces weak fluid inertia. (b) Vertical translation yields a stronger inertial response. (c) Rotation around the center generates a distinct flow field. (d) General motion results from a linear combination of the six fundamental modes that correspond to the six degrees of freedom of motion (Eq. (\ref{['eq:decomposition']})).
• Figure 4: Illustration of the relative flow around a rigid body. (a) Potential flow $\nabla \phi$ induced in the world frame by the body's motion. (b) Rigid body velocity field in the opposite direction, shown in the body frame. (c) Superposition of (a) and (b) yields the flow past the body in the body frame. (d) We assume a small wake region where the surface slip velocity $\mathbf{u}_s$ effectively vanishes.
• Figure 5: Surface slip velocities $\mathbf{u}_s$ (Eq. (\ref{['eq:slip_projection']})) resulting from rigid body motion $(\mathbf{w}, \mathbf{v})$ for an elliptical body (3D-view). (a) Horizontal velocity. (b) Vertical velocity. (c) Rotation induces antisymmetric slip velocities. (d) A linear combination of the previous velocities. Colors indicate velocity magnitude from blue (low) to red (high). Larger slip velocities induce a larger dynamic pressure on the surface.