Bifurcation analysis in aerodynamic, mechanical, chemical, and biological systems is a very important tool for getting an insight into system’s dynamics, predicting its behavior, and designing controllers. Multiple works in many areas of science are devoted to bifurcation analysis. Numerical packages for creating bifurcation diagrams for systems that are too complex for analytical representation (computation of Jacobian) have been developed, e.g. MATCONT. Bifurcation analysis for the skydiver model has proved to be tricky and is yet to be formalized.
This task is very exciting due to the high dimension of the parameter space: the multiple body DOFs, the muscle tension in multiple limbs, and the damping moment coefficients. With so many variables and high nonlinearities and strong longitudinal-lateral coupling in the model even computing the equilibrium points becomes very challenging. The MATCONT package seems to have many limitations when dealing with such cases. It seems that one possible approach to bifurcation analysis of the skydiver model is utilizing our knowledge of movement patterns to reduce the number of control parameters and the dimension of the state space.
From experiments we know that novices exhibit oscillations (stable and unstable limit cycles) around longitudinal and frontal axes, until they learn to control their muscle tension and aerodynamic moments damping. Therefore, the first research activity could be finding the Hopf bifurcation as a function of damping pitch and roll moment coefficients, for the neutral body posture (which can be unsymmetrical for novice skydivers).
