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In industrial context, admittance control represents an important scheme in programming robots for interaction tasks with their environments. Those robots usually implement high-gain disturbance rejection on joint-level and hide direct access to the actuators behind velocity or position controlled interfaces. Using wrist force-torque sensors to add compliance to these systems, force-resolved control laws must map the control signals from Cartesian space to joint motion. Although forward dynamics algorithms would perfectly fit to that task description, their application to Cartesian robot control is not well researched. This paper proposes a general concept of virtual forward dynamics models for Cartesian robot control and investigates how the forward mapping behaves in comparison to well-established alternatives. Through decreasing the virtual system's link masses in comparison to the end effector, the virtual system becomes linear in the operational space dynamics. Experiments focus on stability and manipulability, particularly in singular configurations. Our results show that through this trick, forward dynamics can combine both benefits of the Jacobian inverse and the Jacobian transpose and, in this regard, outperforms the Damped Least Squares method.