A resume of hard work of completing very nice pathfinder project has been published. Pathfinder in 2C has been completed and some results presented to readers. Post contains description of my project’s properties with explanatory videos and images.
Numerical Methods for solving globally convergent nonlinear polynomial system of equations. Pathfinder part 1
There are many applications to solving a set of nonlinear system of equations problem in biology, economics, physics, engineering, geometry (intersection of surfaces) and of course mathematics and we have not found a numerical methods for solving it yet. Because of the existence of several roots, and that these usually are dispersed to unknown positions in N-dimensional space, efficient numerical methods are hard to develop. This posts presents three basics approach in solving this kind of problems and contains one simple example of kinematic chain that is helpful in general understanding of the main problem.
This post explains how differential constraints can be used to implement automatic car parking system. A geometry of parking has been described and explained. Short introduction to mathematical task of deriving differential constraints and solving this problem has been proposed.
This post explains how differential constraints that are widely used in CAD/CAM can be combined with classical mechanics to produce car ESP system that will be manufactured serially and mounted in modern vehicles. Main problems of constraints and conditions of ESP system are explained.