Collision of a Hard Ball with Singular Points of the Boundary

Both the paper and the candidate solution establish that, for a smooth (friction-free) elastic collision of a hard ball with a visible singular point A, the tangential component of the center’s velocity and the angular velocity are preserved while the normal component flips sign, and that the collision is equivalent to a specular reflection of the center off a spherical patch S(A,r) centered at A. The paper derives this via conservation laws with ΔPT = 0, yielding Va_T = Vb_T, ωa = ωb, and Va_N = −Vb_N, and explicitly notes the equivalence to elastic reflection of the center off a sphere patch; the model argues via a normal impulse through the center (zero torque) and the configuration-space erosion Q_r to reach the same reflection law. Hence both are correct, using different proof styles (paper: conservation-law map S; model: impulse/torque plus configuration-space geometry) .