Mass spring model and its coupling with front tracking method

We use a front tracking data structures and functions to model the dynamic evolution of fabric surface. The motion of the surface is modeled by the mass-spring model. The fabric surface is represented by a triangulated mesh. Each vertex point in the mesh represents a mass point and each edge of a triangle represents a spring with preset equilibrium length. The mass-spring system is a nonlinear ODE system. By the numerical and computational analysis, we show that the spring system has an upper bound on the eigen frequency. We analyzed the system by considering two spring models and in one case we proved that all eigenvalues are imaginary and there exists an upper bound for the eigen-frequency. This upper bound plays an important role in determining the numerical stability and accuracy of the ODE system. Based on this analysis, we analyzed the numerical accuracy and stability of the nonlinear mass spring system for fabric surface and its tangential and normal motion. Finally the fabric model is applied to parachute system as the canopy surface.