Abstract
A method for simulating jointed rigid bodies so that swinging joints keep their energy. Each hard joint's constraint gradient is evaluated once at the start of the time step and frozen; the joint pushes only along those directions while the constraint itself is evaluated at the current iterate, so the joint holds exactly at the end of the step (the SHAKE, or constrained Verlet, approach). In augmented vertex block descent each joint force acts along the frozen gradient, and its fixed point is the SHAKE step; in small-step extended position-based dynamics (XPBD) each joint correction moves the bodies along the frozen gradient with SHAKE's Newton denominator. Free motion is made exact as the inertial target: stored velocity is read at the half step, so a constant force yields the exact parabola, and orientation advances by a symmetric splitting of the free rigid body that keeps angular momentum exactly. Together these turn both solvers' joints from implicit Euler, which damps swings, into a second-order, symplectic constrained Störmer-Verlet step.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Recommended Citation
Kimberlin, Kyle, "Rigid-Body Joints Along the Step-Start Gradient", Technical Disclosure Commons, ()
https://www.tdcommons.org/dpubs_series/12439