Modeling and Stability Analysis of Aerially Towed Systems Using Geometric Computational Dynamics

Abstract

This paper presents a method for three-dimensional simulation and analysis of circularly towed cable–body systems with nontrivial coupling between the attitude dynamics of the towed body and the cable. By application of a Lie group variational integrator, a compact and singularity-free geometric model that maintains its accuracy even for extremely long-time simulations with aggressive maneuvers is developed. Coupling the integrator to a nonvariational model of the towing airplane is also discussed. By employing a variation-based linearization technique, a geometric linear system that is used to investigate the mode shapes and the coupling between the motion of the cable and the attitude dynamics of the towed body is obtained. A distributed parameter model is developed separately that describes the equilibrium configurations of the circularly towed system, the results from which are used to evaluate those of the geometric numerical integrator. For the case of towing a bisymmetric finned body, it is observed that reducing the flight path radius leads to a limit cycle, due to the interactions between the rolling motion of the body and the pendulum mode of the cable.