Modelling of two Interconnected Spring Carts and Minimization of Energy

Focus is to form a mathematical model for interconnected spring carts to minimize the energy using Powell's method of minimization. Expressing the energy of a surface in terms of its local deformation, local force on the surface is given by differentiating the energy with respect to position that gives an equation. The modelled equations make a system that has been converted in to a biquadratic function and used to minimize the energy to save the life of spring in the best method of optimization. The Powell's method is given in detail and compared with Downhill Simplex method.