Astolfi, Ortega, and Venkatraman (2010) recently proved the existence of a globally exponentially convergent speed observer for general Euler-Lagrange systems. Key to their result, is a function defined by certain integrals which cannot be solved a priori, and may not have explicit analytic solutions. In this paper, this obstacle to a constructive design is removed and equations that solve the speed observer problem are given in closed form. The design is further simplified by removing up to one third of the observer states used in Astolfi et al. (2010). With the significant reduction in complexity, the new observer is easily applied to estimate the angular velocities in a Furuta pendulum example. (C) 2011 Elsevier Ltd. All rights reserved.