Rigid Body Dynamics with VBD, Section I: Free Bodies

In the VBD paper (SIGGRAPH 2024), we briefly discuss extending Vertex Block Descent to rigid body simulation. The idea is natural: instead of updating a single vertex with 3 DoF, you update an entire rigid body with 6 DoF. But the details matter. This post walks through the full derivation—from the continuous Newton-Euler equations, to discrete backward Euler as a nonlinear system, to the Schur…