# Dynamics Modelling and Simulation for Deployment Characteristics of Mesh Reflector Antennas
## 1 Introduction  
Inherited with merits of large aperture, big shrinkage ratio, and simple topological structure [1; 2], the deployable hoop truss antenna is a significant form of satellite antenna [3]. Furthermore, better accuracy and heat stability are presented in the hoop truss antenna compared with other types. As depicted in Figure 1, the deployable hoop truss consists of front and rear nets, a deployable truss, and a vertical cable. The shape configuration and stiffness of the reflector net are constructed with tensile cable. During the initial state of launch of the antenna, the deployable truss is folded in a shrinkage state due to the capacity of the launch vehicle. As the satellite enters orbit, deployment of the truss is initiated under the action of a torsional spring in the synchronous joint to a certain deployed angle. Then, the driving motor drives the cable penetrating through the inclined rod to continue the following expansion of the antenna. A final deployed configuration is locked by the locking mechanism between the thin inclined rod and thick inclined rod [4]. Dynamics simulation of the hoop truss antenna involved complex dynamic behaviors during on-orbit deployment [5], such as large scale numerical computation, coupling characteristics of the rigid-flexible system, and nonlinearity of clearance impact [6; 7], which pose a challenge to the structural design and controller development of the antenna. Many research studies have been devoted to the investigation on deployment dynamics of the truss antenna in terms of ground test and numerical simulation. [PERSON] et al. conducted a deployment analysis in terms of numerical computation and experiment verification [8]. [PERSON] et al. studied the dynamics of truss without a cable net based on the experimental setup [9]. A ground experiment performed by [PERSON] et al. indicated that the attenuation of driving forces caused by friction effect would induce asynchronous deployment [10]. By contrast with the high economic cost of the ground test, numerical simulation on deployment dynamics provides access to a reliable and economic design of the deployable truss antenna. Deployment analysis of a ring truss under a pre-designed trajectory was researched [11]. Several mechanical models of deployable antennas have been proposed, such as finite element [12], elastic catenary element [13], and spring-damp element [14; 15], to predict the dynamic behaviors of large deformation, contact impact, slack, and wrapping during deployment. Despite the fact that a state of slack or tensile can be captured by the elastic catenary element [13], the condition of the quasi-static process was needed. However, the adopted assumption of finite rotation in conventional finite element could not precisely describe the large deformation [16] of the mesh reflector. Under the assumption of small deformation [17], the influence of truss flexibility was considered in the synchronous deployment of an AstroMesh reflector. [PERSON] et al. analyzed the optimal deployment of a radar antenna using the finite element method under the assumption of infinite small rotations [18], in which the mode component synthesis was adopted to reduce computational cost. A modified deployment planning method was proposed in [17], in which the tension of the cable net is acquired by a simplified model. To describe the large deformation of the flexible body undergoing large scale motion, two main methodologies were developed: co-rotational coordinate formulation [19] and global coordinate formulation. In detail, the latter can be categorized as theory of geometric accuracy [20], isogeometric analysis [21], and absolute nodal coordinate formulation (ANCF) [22]. Due to the advantage of the gradient vector of a particle being assumed as node coordinates, the dynamic behavior of large deformation can be described precisely by an ANCF element. Additionally, the mass matrix obtained by ANCF possesses the metric of constant and the Coriolis item vanishes.