Efficient tethered aerostat model formulation using non-recursive and recursive rigid body dynamics

A computationally efficient discrete model for low strain tethers used in many engineering applications is developed without the use of elastic elements. The tether is modeled using N links, with each link treated as a body of revolution where it is assumed the tether spin is negligible to the dynamics, resulting in each link having only two degrees of freedom. A recursive algorithm is developed for the dynamic equations, with the solution procedure being an order N method requiring only a 2 by 2 matrix inversion, resulting in approximately half the computations of the general recursive algorithm. A comparison between the proposed efficient recursive rigid body model and a lumped point mass model shows the absence of stiff elastic elements eliminates high frequency axial vibrations that appear in many lumped point mass tether models. Absence of high frequency axial vibration facilitates numerical integration of the equations, providing further improvements in computational speed. Furthermore, actual data acquired from UAHuntsville's Optical Tracking Laboratory (OTL) validates the proposed model.;A tethered aerostat model is developed using the proposed recursive tether model. The tether is attached to a 6 degree of freedom aerostat model using a single visco-elastic element. The final recursive tether-aerostat model is well suited for a variety of trade studies required for design and analysis of such systems due to its low computational cost and numerical robustness. Simulations are used to show how the proposed recursive model can be used to investigate the dynamic response and tether loads for a 17 m tethered aerostat in response to varying winds.