Study of a self-impacting double pendulum

A double pendulum with a stopper at the lower joint, as in a mammalian leg, has been studied. The impact has been modelled in a computationally efficient manner using a spring–damper in combination with a logistic function. An estimate of the coefficient of restitution of the impact based on stiffness and the damping coefficient has been developed. The response and stability of the above system have been inspected through simulations with varying coefficients of restitution. The decay rate of energy and angular momentum show dependencies unique to the case on hand.