# Research on the Dynamics of the Space Tubular Expandable Structure Driving Deployment Unit
###### Abstract
To overcome these limitations, the Floating Frame of Reference method (FFR) [17] was proposed, introducing inertial coupling between the motion of rigid components and elastic deformation. However, the nonlinearity of its system matrix significantly impacts the solution of dynamic equations [18; 19], leading to reduced accuracy in solving deformation problems. To address these issues, [PERSON] proposed the absolute nodal coordinate formulation (ANCF) [20; 21] based on finite element and continuum mechanics theories. In ANCF, the nodal coordinates of elements are represented by position vectors and slope vectors, instead of the traditional nodal angular coordinates used in finite elements. Additionally, ANCF derives a constant mass matrix, and its system dynamic equations do not include Coriolis and centrifugal force terms, which improves computational efficiency. Therefore, these advantages make the absolute nodal coordinate formulation more suitable for flexible multibody systems compared to other traditional methods. [PERSON] from Northwestern Polytechnical University [22] conducted in-depth research on flexible beam structures using the absolute nodal coordinate formulation (ANCF). The study focused on modeling flexible beams, numerical solutions of the differential-algebraic equations for multibody systems, and applications. The research proposed a novel multibody system modeling method that considers pin joints, effectively addressing the rigid-flexible coupling dynamics problem in spacecraft solar panels and flexible caterpillar tracks with pin joints. [PERSON] [23] aimed to address the numerical simulation issues of slender thin-walled beams with different cross-sectional shapes under large rotations and deformations. Within the framework of the absolute nodal coordinate formulation, a new method was proposed, employing Lagrange interpolation to construct the displacement field of thin-walled beam cross-sections. [PERSON] from Harbin Institute of Technology [24] conducted research on dynamic modeling, analysis, and motion control of typical flexible attachments in spacecraft, such as large trusses and robotic arms, based on the absolute nodal coordinate formulation. The study validated the applicability of the absolute nodal coordinate formulation in modeling flexible components, providing valuable insights into the behavior of such structures. [PERSON] and colleagues [25] developed a more accurate deformation reconstruction method based on the absolute nodal coordinate formulation, allowing for further extension in the application direction using existing mechanical tools. The method was optimized using a planar beam as an example, and the results demonstrated that the absolute nodal coordinate formulation is beneficial for improving optimization accuracy and efficiency. [PERSON] and colleagues [26] proposed a new formulation of the absolute nodal coordinate formulation (ANCF) for hyperelastic thin shell finite elements based on the Kirchhoff-Love theory. The study derived the two-dimensional compressible Neo-Hookean constitutive model and the two-dimensional incompressible Mooney-Rivlin constitutive model for ANCF shell elements under plane stress conditions. Additionally, they utilized continuum mechanics to derive efficient analytical formulas for the internal forces and their Jacobians within the shell element, enhancing the understanding and analysis of hyperelastic thin shell structures. [PERSON] and colleagues [27] presented a unified modeling method for large-scale flexible space structures based on the absolute nodal coordinate formulation. By employing Kronecker products to express various ANCF element shape functions in a unified form, the study derived motion equations through the Hamilton's principle. This approach provides a versatile and systematic approach to modeling large-scale flexible structures, aiding in their design and analysis. [PERSON] and colleagues [28] proposed a mechanical analysis model suitable for flexible structures based on the absolute nodal coordinate formulation.