In this paper, an advanced study covering the comparison between two classes of generalized inverses is conducted. Two sets of instances, strictly derived from the recently introduced nonunique S- and σ-inverse, are analyzed, especially in terms of degrees of freedom-oriented interchangeable application in different engineering tasks. Henceforth, the respective collections of right and left inverses can be combined in order to achieve a complex tool for robustification of a plethora of real processes. The great potential of two S- and σ-inverse, in particular in robust control and signal recovery as well as complex optimal tasks, is confirmed in the manuscript and supported by the recently carried out research investigations.

The main objective of this article is to obtain equations of motion of the spin–stabilized projectile in the presence of non–constant wind. Introducing models allowing utilization of inhomogeneous wind is dictated by new possibilities created by the use of e.g. lidars in the Fire Control Systems (FCS). Constant feed of wind data can replace meteorological messages, increasing the FCS effectiveness. Article contains results of projectile flight simulations which indicate the positive effect that the derived explicit form of the model has when considering software development for modern Fire Control Systems.