M. A. Ghapanvary - Department of Aerospace Engineering ,Malek-Ashtar University of Technology, Tehran, Iran
M. Nosratollahi - Department of Aerospace Engineering ,Malek-Ashtar University of Technology, Tehran, Iran
J. Karimi - Department of Aerospace Engineering ,Malek-Ashtar University of Technology, Tehran, Iran

This paper is concerned with the dynamic stability study of a gliding parachute-payload system along its gliding path. To scrutinize the respective dynamic response characteristics after releasing from high altitude, a modified multi-body model is developed. In the stability analysis procedure, the yawing motion of the payload is considered in system dynamics, which in turn creates a state-dependent matrix in the stability analysis and makes the linearization algorithm more cumbersome. To solve the problem, a unified Jacobian-based symbolic differentiation algorithm is implemented and the dynamics is linearized about various operating points along gliding segment of a typical planned trajectory. Based on results, the system has short period and phugoid modes in longitudinal channel just like an aircraft. In addition to dutch roll mode, the system has a low frequency coupled roll-spiral mode in lateral-directional channel which is a result of effective canopy anhedral angle. It is shown, the coupled mode can be decomposed into two distinct roll and spiral modes for small anhedral angles. Based on results, as the parachute descends, both the period and damping ratio for the short period mode were increased by ۱۸ and ۳۰%, respectively. For the phugoid mode the period of oscillations is decreased by ۲۰% and the damping ratio, almost remains constant. For the lateral-directional channel,. As the parachute descends, the dutch roll mode is destabilized whereas the other modes are stabilized. Furthermore, from a practical point of view, lengthening the suspension lines stabilizes the coupled roll-spiral mode whereas destabilizes the other modes.

Multi-body System, Dynamic Response, Anhedral Angle, Gliding Path