arXiv subjects
Publications and source records attributed to V. Yu. Tertychny-Dauri.
The following offers a new axiomatic basis of mechanics and physics in their most important dynamics domain, i. e. an axiom (principle) of completeness intended to generalize Newton's second law of motion for the case of a non-stationary variable-mass point (system) that varies with time. This generalization leads to hyperdynamic dependencies describing such motion from new accurate qualitative standpoints.
The article deals with the subject of solving the problem of canonical-map synthesis for Hamiltonian systems. For this purpose, the controlling-function method has been developed that allows appropriate changes of the variables in terms of calculus of canonical variation, starting from their target conditions. To use the canonical formalism, the initial dynamic system that employs changing Lagrange multipliers is reduced to a Hamiltonian system in an xpanded phase space, followed by the construction of controlling function. The algorithm suggested for the canonization of controlled mappings has an advantage over the known procedures, and first of all, redundancy in the rocedure that chooses regulated coordinate transformations as a base for a goal-seeking synthesis scheme.