Torsional springs play a crucial role in the dynamics of systems involving rotation, such as the rolling motion of aircraft. These springs exert a restoring torque proportional to the angular displacement from their equilibrium position, which in this case, is the wings' rest position relative to the fuselage. The spring's stiffness is denoted by the parameter , which indicates how much torque is generated for a given angular displacement . This relationship is expressed by the torque formula:
In this equation, the negative sign signifies that the torque works to counteract the displacement, thus attempting to restore the wings to their original position. Understanding torsional springs is essential for modeling how the aircraft responds during maneuvering by assessing the generated torques and how they influence motion.