Coefficient of restitution and linear dashpot model revisited

With the assumption of a linear-dashpot interaction force, we compute the coefficient of restitution as a function of the elastic and dissipative material constants, k and gamma by integrating Newton's equation of motion for an isolated pair of colliding particles. It turns out that an expression e(k,gamma) widely used in the literature is even qualitatively incorrect due to an incorrect definition of the duration of the collision.