Long-term dynamic modeling of tethered spacecraft using nodal position finite element method and symplectic integration

Coupled Orbital-Attitude Dynamics Of Flexible Electric Solar Wind Sail

“…is the nodal coordinate vector with subscripts referring to the node numbers of the kth element, Nk is the shape function matrix defined in [11,12] From the Hooke's law, the elastic stress of k-th element can be written as,…”

“…where Ke,k is the nonlinear element stiffness matrix and , kk F is the generalized nodal force vector resulting from the elasticity of element in the global inertial coordinate system [11,12].…”

“…The dynamic equations of E-sail can be obtained by assembling Eq. (9) with the standard assembly procedure in the finite element method [12,13]. It is worth pointing out that the primary variables in the NPFEM are the nodal position coordinates instead of the nodal displacements in the conventional finite element method.…”

“…It discretizes the continuous tether into a finite number of elements to approximate the solution within each element. The main advantage of the finite element method over the lumped method is its capability to handle the complex geometries with different tether properties along the tether length in an algorithmic fashion [11,12].…”

Debris Rotation Analysis During Tethered Towing for Active Debris Removal

“…In [23], Li, Zhu, et al, analyse the dynamics of the electrodynamic tethers and show that the thermal effects affect the stability of the current-conducting tethers. The authors in [25] address the challenges of accurate and robust time integration methods applied to the space tethers dynamic models.…”