## 1 Introduction  
High-altitude long-endurance (HALE) aircrafts, which are being considered for aerial reconnaissance, long-time surveillance, environmental sensing and communication relays, have been the topic of modern flying vehicles [1]. Due to the energy and weight restrictions, HALE aircrafts, especially solar-powered aircrafts, notably feature very low wing-loading and ultra-light wing structure with high aspect-ratio. The long and slender wings inherently have relatively low structural stiffness, which gives rise to large geometrically nonlinear deformations during normal flights. The aerodynamics, inertia distributions and even the thrust locations and directions could be significantly affected, resulting in the changes of aeroelastic characteristics, trim conditions and the overall flight mechanics of the whole aircraft. The mishap of Helios Prototype in 2003 is a typical result brought by the complex interactions among multiple disciplines and the lack of adequate analysis tools [2]. Thus, a simple yet realistic model and analysis framework that can accurately assess the flight performances of a largely deformed highly flexible aircraft, and can fully account for the coupling between flight dynamics and both structural nonlinearity and unsteady aerodynamics, which play a key role in the vehicle's static and dynamic characteristics, are of paramount importance in the analysis and design of these highly flexible aircrafts [3; 4; 5]. Such models are typically built using nonlinear beam representations of the structure [6; 7; 8], with either unsteady strip theory [9; 10; 11; 12; 13] or unsteady vortex lattice aerodynamics [14; 15]. [PERSON] [16] pointed out that many kinds of analyses with different models and complexities can be applied to investigate the aeroelastic characteristics of a flexible aircraft. Firstly, with the linear stiffness and mass matrices, an eigenvalue analysis can be conducted to know the structural natural mode shapes and frequencies of the unloaded aircraft, which are the basics of further dynamic studies. Secondly, the aircraft can be trimmed by a nonlinear static aeroelastic approach to get the deformed positions under given aerodynamic loads, thrusts and gravity. Then, the aeroelastic equations can be linearized and eigenvalue analysis be conducted about this equilibrium state, which will give a more reasonable estimation of the stability of the deformed flying vehicle. However, in many cases, especially when the wing-loading and structural stiffness of the aircraft are low enough, such a linear stability analysis based on the hypothesis of small disturbance cannot give a precise prediction to the nonlinear dynamic responses of a flying aircraft under large disturbances. Thus, the final option to analyze the responses of a flexible aircraft is the direct solution of the nonlinear aeroelastic equations via time-marching numerical integration. This kind of analysis will give responses of an aircraft as a function of time, which can be considered as the realistic indications of its dynamic behaviors. To investigate the nonlinear aeroelastic responses, trim solutions and flight stability of a complete highly flexible aircraft, [PERSON] and [PERSON] [17] developed an analysis package named NATASHA (Nonlinear Aeroelastic Trim and Stability of HALE Aircraft). In their framework, the [PERSON] Peters' finite state unsteady aerodynamic theory is used to calculate the aerodynamic loads. The geometrically exact fully intrinsic equations are used to model the highly flexible structure of the aircraft. With all the variables defined in the local reference system, the computational costs of coordinate transformation and assembly of global tangential stiffness matrix are reduced, with which the solution efficiency is improved. Their studies on a typical flexible flying-wing aircraft show that there are significant differences in flight dynamic characteristics between the deformed and undeformed aircraft.