Recently, 3D gait simulations were generated by solving optimal control problems using musculoskeletal models. However, these simulations lack predictive power and require long computation time. We formulated implicit dynamics for a full-body 3D musculoskeletal model to solve optimal control problems in a computationally efficient way. We show that with the implicit formulation a full-body predictive simulation of curved running can be generated from a random initial guess in about two hours.