Variational Principle of Extremum in Electromechanical and Electrodynamic Systems

Variational Principle of Extremum in Electromechanical and Electrodynamic SystemsHere we shall formulate and prove the variational optimum principle for electromechanical systems of arbitrary configuration, in which electromagnetic, mechanical, thermal, hydraulic or other processes are going on. The principle is generalized for systems described by partial differential equations, including also Maxwell equations. The presented principle permits to expand the Lagrange formalism and extend the new formalism on dissipative systems.

Here we shall formulate and prove the variational optimum principle for electromechanical systems of arbitrary configuration, in which electromagnetic, mechanical, thermal, hydraulic or other processes are going on. The principle is generalized for systems described by partial differential equations, including also Maxwell equations. The presented principle permits to expand the Lagrange formalism and extend the new formalism on dissipative systems. It is shown that for such systems there exists a pair of functionals with a global saddle point. A high-speed universal algorithm for such systems calculation with any perturbations is described. This algorithm realizes a simultaneous global saddle point search on two functionals. The algorithms for solving specific mathematical and technical problems are cited. The book contains numerous examples, including those presented as M-functions of the MATLAB system and as functions of the DERIVE system.