Dynamics and control of single-line kites

This paper presents a dynamic analysis of a single-line kite with two degrees of freedom. A Lagrangian formulation is used to write convenient equations of motion. The equilibrium states of the system and their stability are studied; Eigenvalues and eigenmodes are calculated by using linear theory. The stability in the parametric plane delta - W-o is discussed, where delta defines the bridle geometry and W-o is wind velocity. The system goes through a Hopf bifurcation and periodic branches of solutions appear. The orbits and their stability have been calculated numerically using Floquet theory and wind velocity seems to play an important role in their existence. Finally the kite response against gusts is considered and an open loop control system developed to keep the flight altitude invariant under changing atmospheric conditions. Modifying the bridle's geometry seems to be a convenient way to control a kite's performance.