Dynamical modeling of deployable electrodynamic tethers using geometric mechanics

This study presents a comprehensive dynamic modeling framework for deployable electrodynamic tether systems using geometric mechanics. The forced Euler-Lagrange equations governing the electrodynamic tether dynamics are derived by Hamilton's principle of least action. The discrete-time equivalent of these equations are then obtained by the application of the discrete variational mechanics approach. As a result, a forced Lie group variational integrator is developed that ensures the preservation of the geometric properties of the configuration space. The proposed integrator guarantees long-term numerical accuracy and stability, particularly in the presence of non-conservative forces such as the Lorentz force and aerodynamic drag, as well as control inputs. Furthermore, the discrete-time Euler-Lagrange equations of the tether systems are linearized in the vicinity of their stable equilibrium state by variational linearization to derive the geometric Jacobian of the linearized system. This linearized framework allows for a detailed examination of the system's modal frequencies and mode shapes. Numerical simulations demonstrate the exceptional accuracy and robustness of the proposed variational integrator in capturing the complex dynamics of electrodynamic tethers and tether deployment. The findings highlight the integrator's superior performance in maintaining numerical stability, making it a valuable tool for high-precision simulation and analysis of deployable electrodynamic tether systems. • Modeled dynamics of deployable electrodynamic tether systems by geometric mechanics. • Proposed a forced Lie group variational integrator for electrodynamic tether systems. • Studied EDT libration modal frequencies and mode shapes by geometric Jacobian theory. • Demonstrated high precision and robustness of the integrator by numerical simulation.