This video showcases a custom-built robotic platform alongside its differentiable digital twin, developed within Ostrich, a GPU-accelerated differentiable simulation environment. The demonstration highlights how real-world robotic systems can be synchronized with high-performance simulation to enable large-scale learning, real-time estimation, and advanced control in challenging environments. Ostrich is a differentiable rigid-body simulator that resolves hard contacts and friction using non-smooth Newton iteration at an integration step of 0.1 s. By differentiating through the converged residual via the implicit function theorem, the simulator computes adjoints with O(1) memory per timestep.