Predictive simulation of human movement is a key tool in biomechanics and assistive device design, enabling the exploration of scenarios difficult to study experimentally. These simulations are typically formulated as optimal control problems, where muscle excitations and actuator inputs are determined to minimize physiological or task-related costs while satisfying the equations of motion. When realistic interactions with the environment or devices are included, musculoskeletal models involve non-smooth phenomena such as unilateral contact, impacts, friction, and kinematic constraints, which challenge numerical integration and optimization. We investigate gradient-based optimal control methods for musculoskeletal multibody systems with non-smooth dynamics. Our framework uses the open-source software Odin, which applies a finite-element-like formulation of multibody dynamics, enabling modular modeling of systems with closed kinematic loops and assistive devices. Hill-type muscle models are integrated, while OpenSim is used for pre- and post-processing. Non-smooth interactions, such as foot-ground contact or human-device interfaces, are modeled using constraint-based formulations enforcing non-penetration and impact laws. The resulting hybrid dynamics—smooth phases governed by differential-algebraic equations with instantaneous velocity jumps—are handled with a non-smooth generalized-alpha time-stepping scheme. Gradients are obtained consistently by differentiating the time-stepping scheme and exploiting tangent operators from semi-smooth Newton iterations. Mathematically, trajectories of non-smooth systems are not differentiable, challenging gradient-based optimization. However, non-smooth events usually occur at isolated instants, while much of the motion remains smooth. Gradients from discretized dynamics can still provide useful descent information. To reduce discontinuity effects, a multiple-shooting formulation is used, focusing on non-smooth event localization. Regularized contact formulations are also explored for initial guesses. The framework is evaluated in contact-rich applications, including predictive simulations of prosthetic gait and human-exoskeleton interaction, demonstrating its potential for realistic, optimization-based musculoskeletal modeling.