## 1 Introduction  
The deployable spatial truss structure is a typical flexible multibody system consisting of beam members. With the increase of the size, the deployable spatial truss structure usually undergoes finite deformation when refer to finite displacement and rotation. The most common modeling methods in flexible multibody system for beams are the Absolute Nodal Coordinate Formulation (ANCF) and the Geometrically Exact Beam Theory (GEBT). Both approaches can provide the solution of finite deformation and finite motion. The ANCF, proposed by [PERSON] [1, 2], is one of the methods aimed at multibody system dynamics areas recent years. The method uses slopes instead of infinitesimal rotations to simplify the parameter updating algorithm, but at the cost of introducing more degrees of freedom, which reduces the computational efficiency. Comparisons of ANCF and GEBT have been accomplished by [PERSON] [3] and [PERSON] et al. [4]. To reduce the computational cost, the latter is employed in this work. The geometrically exact beam theory (GEBT) is also known as the Simo-Reissner beam theory, which was initially proposed by [PERSON] [5,6] and then developed by [PERSON] [7, 8, 9] and other pioneers; for example, [PERSON] and [PERSON] [10], [PERSON] et al. [11], and [PERSON] and [PERSON] [12,13]. In GEBT, the compositions of translations and rotations are typically uncoupled in the space of \(\mathbb{R}^{3}\times SO(3)\). The cross-section position is considered in the linear space \(\mathbb{R}^{3}\), while the rotation belongs to a nonlinear space, the special orthogonal group \(SO(3)\). In general, the incremental position and rotation variables are described in the global frame, thereby leading to a strong rotational nonlinearity. Based on the classical GEBT, describing the finite rotation variables in the local frame can reduce the rigid rotational nonlinearity. It is implied that the iteration matrix corresponding to the rotation parameters in the initial configuration can be maintained in the simulation, which drastically improves the computational efficiency, especially for the multibody systems, which undergo large displacement and rotation. For cases of finite strain and material nonlinearity, the extension of GEBT can be found in [14,15] based on the Geometric Continuum Mechanics. An obvious feature of a multibody system is that the connection between different bodies is usually achieved through some joint constraints, such as spherical joint, sliding joint, etc. More different types of classical joint constraints can be found in [16]. For a majority of spatial deployable structures, the sliding joint is often applied and plays an important role. The most common method in defining the friction-free sliding is the Lagrangian multiplier method. Employing this method, [PERSON] and [PERSON] [17,18] formulated the sliding joint based on the GEBT and pointed out the difference between the prismatic joint and sliding joint, while [PERSON] et al. [19] and [PERSON] and [PERSON] [20] modeled the sliding joint applying ANCF. However, the Jacobian matrix of the sliding joint constraint equation is not found in [17,18]. More application of the Lagrangian multiplier on the problems can be found in [21,22]. Besides, there are different methods being employed in modeling sliding joint, such as the master-slave method [23]. Moreover, the Lagrange basis functions have always been applied for finite element discretization in such research, which gives rise to the gap between computer-aided design (CAD) and computer-aided engineering (CAE). The isogeometric analysis (IGA), which was introduced in 2005 by [PERSON] et al. [24], is filling the traditional gap between CAD and finite element solvers. Over the last decade, IGA has become a well-established method used in structural modeling [25, 26, 27]. The application of the non-uniform rational B-splines (NURBS) basis functions is shown to be much more advantageous than conventional finite element analysis [28,29].