Formalizing Mechanical Analysis Using Sweeping Net Methods I

Published with thanks to Yahowah, Yeshua Ben Joseph - the living one Allaha. In memory of our cat, Lazy. This paper proposes a method for approximating surfacing singularities using sweeping nets. By constructing a densified sweeping subnet for each individual vertex of a saddle map and combining them, we create a complete approximation of the singularities. We define functions $f_1$ and $f_2$, which are used to calculate the charge density for each subnet. The resulting densified sweeping subnet closely approximates the surfacing saddle map near a circular region. We apply sweeping net methods to formalize the mechanical analysis for analytical methods, providing detailed proofs and explanations of the underlying mechanics.