By Ruggero Maria Santilli
In the previous volume,l I pointed out invaluable and adequate stipulations for the life of a illustration of given Newtonian structures through a variational precept, the so-called stipulations of variational self-adjointness. a main aim of this quantity is to set up that each one Newtonian platforms pleasing definite locality, regularity, and smoothness stipulations, even if conservative or nonconservative, might be taken care of through traditional variational ideas, Lie algebra innovations, and symplectic geometrical formulations. This quantity hence resolves an issue at the repre sentational functions of traditional variational rules that has been 2 lingering within the literature for over a century, as said in Chart 1. three. 1. the first result of this quantity are the subsequent. In bankruptcy 4,3 I end up a Theorem of Direct Universality of the Inverse challenge. It establishes the life, through a variational precept, of a illustration for all Newtonian structures of the category admitted (universality) within the coordinates and time variables of the experimenter (direct universality). The underlying analytic equations turn into a generalization of traditional Hamilton equations (those with no exterior phrases) which: (a) admit the main basic attainable motion sensible for first-order platforms; (b) own a Lie algebra constitution within the such a lot basic attainable, common recognition of the product; and (c) 1 Santilli (1978a). As used to be the case for quantity I, the references are indexed on the finish of this quantity, first in chronological order after which in alphabetic order.