Regarding computation of dynamics and its derivaties for infeasible states

[marginallyunstable]

Hi Simple Team,

I went through the papers of your group:

• From Compliant to Rigid Contact Simulation: a Unified and Efficient Approach and
• Highly-Efficient Differentiable Simulation for Robotics

I was wondering, for rigid bodies contact simulation, what happens if i provide a "infeasible" state to the simulator. For example, consider the equations (5) and (6) from the paper: Highly-Efficient Differentiable Simulation for Robotics. If i provide states of the rigid bodies such that they are interpenetrating, what would the solution of solving equations (5) and (6) be? Is it that, what will happen eventually is that, the infeasible state will be projected to a "nearest" point in the feasible non-penetrating set, and (5) and (6) are calculated thereon? Also, what happens to the derivatives of the dynamics in this case?

I would really appreciate your help in understanding this.