## 1 Introduction
[16] investigated the installation of heavy objects with the pendulum method using nonlinear time-domain coupled analysis techniques, highlighting the significant impact of surface vessel motion on the cables and the critical role of the center of gravity and buoyancy of the heavy objects in overall motion. [PERSON] et al. [17] performed experimental studies, examining the flutter of hinged vertical plates caused by uniform fluid resistance during the pendulum installation process, and proposed a redesigned heavy object shape to reduce the oscillation during the PIM swinging process. [PERSON] et al. [18] carried out numerical simulations on the Dual Cap-X pendulum installation process, investigating the effects of certain key parameters on operability. [PERSON] et al. [19] performed a risk analysis of the subsea heavy object pendulum installation process based on operational safety analysis and risk assessment, viewing it as a high-risk phase of accidents. They underscored the necessity for further mechanical analysis of the entire pendulum installation system, particularly with regard to the effect of dynamic tension changes in the cables with depth during deployment. Figure 1: Flowchart of cantilever deployment. However, existing research has inadequately addressed the characteristics of inertia, large deformations, and large rotational angles of cables with flexible properties during continuous pendulum processes. A review of the literature reveals that, although most traditional dynamics analysis methods [20] such as the finite element method in SESAM, the lumped mass method in OrcaFlex, and the finite difference method endeavor to simulate flexible structures, they predominantly rely on small deformation assumptions and thus may overlook significant post-deformation changes. This oversight can result in neglecting the impact of deformation coupling terms in the dynamics of large deformation systems. [PERSON] et al. [21] highlighted the challenges in directly applying traditional methods to analyze large deformations, particularly when integrating these coupled deformation quantities with large deformation movements. Therefore, it is imperative to utilize appropriate numerical analysis methods to enhance the accuracy of simulations of the pendant deployment process. To address the limitations of nonlinearity in large deformations inherent to traditional finite element methods, [PERSON] et al. [22] introduced the Absolute Nodal Coordinate Formulation (ANCF). This formulation utilizes global coordinates and directional derivatives to determine element positions, and foregoes the use of Euler angles, eliminating the effects of Coriolis and centrifugal forces in large deformations and enabling inertial forces to be expressed in a linear form while maintaining a constant mass matrix. After years of continuous refinement and improvement, the Absolute Nodal Coordinate Formulation has proven to offer high precision and stability in practical analysis [23; 24; 25]. Recently, [PERSON] et al. [26] demonstrated that numerical solutions based on ANCF elements for three-dimensional elastic fiber soft tissue modeling exhibit higher accuracy than those obtained with ANSYS. [PERSON] et al. [27] proposed three-dimensional Rational Absolute Nodal Coordinate Formulation (RANCF) fluid elements based on cubic rational Bezier volumes, and the simulation results aligned with the existing literature, confirming the accuracy and feasibility of this method. The advancement of the ANCF method has laid a solid foundation for its application in fields such as marine engineering. For example, [PERSON] et al. [28] demonstrated the effectiveness of the ANCF method in determining the static and dynamic characteristics of large deformation flexible deepwater structures by analyzing rigid lazy-wave catenary risers. [PERSON] et al. [29] conducted a comprehensive Absolute Nodal Coordinate Formulation (ANCF) coupled analysis of ROVs. [PERSON] et al.