# Application of Absolute Nodal Coordinate Formulation in Calculation of Space Elevator System
## 1 Introduction  
As a potential new space transportation system for transporting the payload to outer space, the main structure of the space elevator system mainly consists of four parts: ground anchor point, rope, climber and zenith anchor. The whole system relies on the centrifugal force generated by the rotation of the earth to keep the system stable and transport the payload through the climber. The concept originated from the invention of [PERSON], and was cemented in engineering terms by [PERSON] [1]. It was not possible to obtain the desired strength of the tether material until the discovery of carbon nanotubes [2]. At the end of the 20 th century, NASA established a research group led by Dr. [PERSON] and demonstrated the feasibility of the space elevator system [3]. To fully understand the potential commercial application of space elevator, the International Space Elevator Association (ISEC) introduced the concept of Galaxy port [4]. Through the life cycle assessment of the space elevator, [PERSON] [5] found that the design of the space elevator is an environmentally and economically sustainable choice for rail transportation. [PERSON] [6] studied the dynamics of a partial space elevator system with multiple climbers and applied the optimal control to develop optimal operation modes to suppress the liberation of the partial space elevator. [PERSON] [1] established the continuous static model of a rope element based on differential equations, and first deduced the gradual function model of the rope's cross-sectional area. However, the elasticity of the rope was not considered, so [PERSON] [7] and [PERSON] [8] established the system static equilibrium equation considering the rope elasticity on thebasis of Pearson, deduced the cross-sectional area gradient function model of the equatorial space elevator elastic rope, and conducted relevant research on the system parameter of the gradient section space elevator system, which laid the foundation for the subsequent research on the dynamics of the space elevator system. The rigid rod tether model has fewer degrees of freedom and simple analysis. [PERSON] [9] studied the stability characteristics of the space elevator system near the equilibrium point based on the small angle hypothesis through the rigid rod tether model. The chain rod model discretizes the continuous rope into a system composed of finite rigid rods or elastic rods [10]. [PERSON] [11] used the chain rod model to study the stress of some space elevator systems, and explored the influence of climbers on the vibration law of some space elevator systems. The lumped mass tether model discretizes the rope model into a series of mass points connected by spring dampers, simulates the axial stiffness of the rope through the elasticity of the spring, and reflects the flexibility of the rope with the rotation angle of the adjacent spring. Based on the lumped mass tether model, [PERSON] [12] studied the vibration influence of the climber on the space elevator system, proposed the relevant control strategy, and carried out the modal analysis of the system. [PERSON] [13] carried out a dynamic modeling of deployment latitude based on the \"chain-bar\" tether model and lumped mass tether model, respectively, and studied the deployable latitude range of non-equatorial space elevator system. Neither the \"chain-bar\" nor the lumped mass tether model can truly reflect the constitutive mechanical characteristics of the flexible rope, and cannot accurately describe the large deformation movement of the flexible rope. A high number of elements is necessary to ensure the accuracy of the model; thus, the simulation calculation is inefficient. [PERSON] [14] proposed the absolute nodal coordinate formulation (ANCF), which is based on the theory of continuum mechanics and mainly solves the dynamics of large deformation flexible bodies.