We study the dynamics and the optimization of the shock deceleration supported by a payload when its airborne carrier impacts the ground. We build a nonlinear elastic model for a container prototype and an elastic suspension system for the payload. W
e model the dynamics of this system and extract information on maximum deceleration, energy transfer between the container and payload, and energy resonant damping. We designed the system and perform lab experiments for various terminal velocities and types of grounds (cement, grass, sand water, etc.). The results are compared with the theoretical model and results are commented, including predictions for deceleration at different types of ground impact. The results can be used for aerial delivery systems, splash-down of capsules, recoveries, weather balloons, coastal surveying systems, or the new introduced goal-line technology in sport competitions.
In Liang et al (2009), the current authors demonstrated that BSDEs can be reformulated as functional differential equations, and as an application, they solved BSDEs on general filtered probability spaces. In this paper the authors continue the study
of functional differential equations and demonstrate how such approach can be used to solve FBSDEs. By this approach the equations can be solved in one direction altogether rather than in a forward and backward way. The solutions of FBSDEs are then employed to construct the weak solutions to a class of BSDE systems (not necessarily scalar) with quadratic growth, by a nonlinear version of Girsanovs transformation. As the solving procedure is constructive, the authors not only obtain the existence and uniqueness theorem, but also really work out the solutions to such class of BSDE systems with quadratic growth. Finally an optimal portfolio problem in incomplete markets is solved based on the functional differential equation approach and the nonlinear Girsanovs transformation.
