Dynamics and Energy Analysis of Nonequatorial Space Elevator Using Three-Dimensional Nonlinear Finite Element Method Extended to Noninertial Coordinate System

Abstract

A space elevator is a futuristic space transportation technology that enables low-cost and versatile payload transportation using climbers on a tether deployed from the geostationary orbit (GEO). In particular, a nonequatorial space elevator, which contains an anchor in a region with latitudes on the Earth, has recently attracted attention. It has several advantages, such as extending the construction range and avoiding collisions with spacecraft in the GEO. Prior research has focused on rigid-body or spring-mass models with low fidelity. This paper proposes a modeling method for nonequatorial space elevators using a nodal-position finite element method (NPFEM) extended to a rotational coordinate system. The NPFEM is a three-dimensional finite element method that considers geometric nonlinearity. Conventional NPFEMs have only been formulated using inertial coordinate systems. This paper proposes a method to formulate the NPFEM in a noninertial coordinate system and derive the inertial forces and Jacobian matrices. In addition, a three-dimensional analysis of a nonequatorial space elevator was performed based on the proposed method. After determining the equilibrium position of the NPFEM, the dynamic response of the tether during climber ascent was analyzed. Moreover, parametric studies were conducted by varying several properties of the nonequatorial space elevator. Furthermore, the energy exchange between the components was analyzed to validate the proposed method and to discuss the energy perspective of the space elevator. The results revealed that the proposed nonequatorial space elevator model experienced a more tensioned equilibrium and exhibited a more significant dynamic response than conventional models.