Tethered Aerostat Modeling Using an Efficient Recursive Rigid-Body Dynamics Approach

Abstract

A tethered aerostat model is developed using a computationally efficient recursive tether model. The recursive rigid-body tether model results in unconstrained ordinary differential equations and maintains much of the simplicity of simple lumped mass tether models while avoiding numerical difficulties associated with using many stiff elastic elements with low mass. Further efficiency is achieved by treating each tether link as a body of revolution and assuming that tether spin is negligible to the dynamics. The tether is attached to a 6 degree of freedom aerostat model using a single visco-elastic element. The final recursive tetheraerostat model is well suited for a variety of trade studies required for design and analysis of such system 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 17m tethered aerostat in response to varying winds. Nomenclature c j a = acceleration of j th connection joint with respect to the inertial frame m j a = acceleration of mass center of j th link with respect to the inertial frame A,B,Q = apparent mass values bj = j th link of the tether (ground link j = 0, root link j = 1, parent body j = jp) cj = j th connection joint (ground connection joint j = 0) cT