Simulation of the dynamics of an electrodynamic tether on a circular inclined orbit shows a very complex motion driven by the electrodynamic forces acting on the conductive tether. These forces depend on the current flowing in the wire, the Earth magnetic field, the orbital velocity and the tether position. In this paper we use a simple model to describe the dynamic effects of these forces. The tether is modeled as a rigid rod with point masses at the ends. We also adopt a non-tilted dipole model for the Earth magnetic field, and we assume that the tether current is constant. When the current is null, the system has a stable equilibrium position with the tether aligned along the local vertical. When the current is different from zero, a periodic motion appears. A nonlinear analysis of the motion shows that the periodic solutions are always unstable (within the limitation of the model considered in the paper). The physical reason for the instability is that the electrodynamic forces pump energy continually into the system. The net energy increase per orbit for the periodic solution (or state space trajectory) is zero. However, any nonperiodic trajectory in its neighborhood has a positive net energy flux per orbit so that after several orbits the in-plane libration becomes a rotation. The mechanism responsible for this instability depends on the orbital inclination. Unlike other destabilizing mechanisms found in electrodynamic tethers, this one is present in any kind of tether system with either a flexible or a rigid tether, operating in the generator or thruster mode and utilizing a bare tether or a large spherical termination to collect the ionospheric electrons. The instability described in this paper is independent of the presence of resonant force components that may be generated by the magnetic and plasma fields.

A new kind of dynamic instability in electrodynamic tethers

Dynamics of a tethered satellite formation for space exploration modeled via ANCF


 Absolute nodal coordinate formulation (ANCF) is a non-incremental nonlinear finite element procedure that has been successfully applied to the large deformation analysis of multibody systems for more than two decades. Although a comprehensive review on ANCF was conducted by Gerstmayr et al. in 2013, significant theoretical developments have been made since then at a much faster pace to improve the element accuracy and computational efficiency. In order to overview recent advances in ANCF simulation capabilities that are not covered in the first review paper, this paper aims to conduct a comprehensive review of 259 papers concerning ANCF published from 2012 through 2020. It is shown that the ANCF element library has grown substantially for beam, plate/shell, solid elements, eliminating drawbacks of ANCF elements developed earlier. The application areas have extended, especially in the aerospace field, and the enhanced ANCF simulation capabilities have been demonstrated in solving challenging engineering problems. Research efforts have been made continually to integrate computer-aided design (CAD) and analysis with ANCF elements. Furthermore, computational improvements and multiphysics simulations have become major research topics for ANCF. It is also demonstrated that the accurate ANCF geometry description can be exploited to facilitate structural optimization of multibody systems.

https://asmedigitalcollection.asme.org/computationalnonlinear/article-pdf/17/8/080803/6871780/cnd_017_08_080803.pdf

Recent Advances in the Absolute Nodal Coordinate Formulation: Literature Review From 2012 to 2020

Deployment of flexible space tether system with satellite attitude stabilization

Symplectic Analysis on Coupling Behaviors of Spatial Flexible Damping Beam

Model predictive control for spin-up maneuver of an electrodynamic tether system

Dynamics of a flexible multi-tethered satellite formation in a Halo orbit with uncertain parameters

Various promising applications of electrodynamic tether have been proposed for space missions over the past decades. A crucial issue of these missions is to deploy an electrodynamic tether under a rapid and stable state. This paper aims to stabilize the libration motions of a bare electrodynamic tether during its three-dimensional deployment. The tethered system under consideration consists of a main-satellite and a sub-satellite connected to each other through a bare electrodynamic tether. A widely used dumbbell assumption considering the tether as rigid and inflexible is adopted to facilitate the dynamic modeling and analysis of the tethered system. A pair of active control laws is synthesized by simultaneously regulating the electric current and tether tension to achieve an efficient stabilization of the three-dimensional libration of the bare electrodynamic tether in the deployment process. Moreover, comparisons of three groups of numerical simulations are performed to evaluate the in uences of orbital inclinations and geomagnetic field models and the performance of the active control laws.

Caoqun Luo

Papers

Dynamics of a tethered satellite formation for space exploration modeled via ANCF

Deployment of flexible space tether system with satellite attitude stabilization

Model predictive control for spin-up maneuver of an electrodynamic tether system

Dynamics of a flexible multi-tethered satellite formation in a Halo orbit with uncertain parameters

Libration control of bare electrodynamic tether for three-dimensional deployment