A referenced nodal coordinate formulation

Abstract

We develop a referenced nodal coordinate formulation (RNCF) to study the dynamics of flexible bodies undergoing large-distance travels and/or high-speed rotations. RNCF is similar to the absolute nodal coordinate formulation (ANCF) but is presented in a noninertia reference coordinate system (RCS). The position vector and rotation matrix of the RCS describe translational and rotational motions of the system, whereas the nodal coordinates and slopes in a structure depict its large deformations, such that the generalized coordinates with multiple scales in length and time are automatically separated. We develop a parameter-irrelevant technique to derive the rotation equations of the system, where the influences of large deformations on the rotatory inertia tensors are embodied. The derived governing equations are simple and elegant, and consistent with the governing equations for rigid bodies, the floating frame of reference method, as well as ANCF. We verify the RNCF approach by three typical examples, including the spin-up maneuver, the high speed motor, and the flexible slider-crank mechanism. The results indicate that to achieve the same accuracy, the computational cost for RNCF is much lower than that for the corresponding ANCF in high-speed rotating systems. Moreover, the electrical solar wind sail spacecraft system is formulated by RNCF, and its propulsive efficiencies with respect to the spin rates of the E-sails are studied by full-scale models with over ten thousand degrees of freedom. RNCF provides an effective way to formulate and study the dynamics of vehicles, trains, ships, aircrafts, and spacecrafts.