Singular Problems in Electric and Mechanics Tasks at Idealization Mathematical Description

The possible dangers of idealization in the process of constructing mathematical images of physical objects or systems are shown. The above is revealed on five practical problems of electricity and mechanics. They may be acceptable, hidden, or even such as reaching singularities, or even unreal. It is revealed on five practical problems of electricians and mechanics.

In particular, it is a question of electric circuits containing EJ-degenerate sections and circuits formed solely by ideal current sources and EMFs, rotational singularity for ideal elasticity, harmonic electrical resonance, external characteristic of a serial steady state generator for the ideal ferromagnetism, the singularity and the paradox of 4/3 electrons. The complete system of equations of the electric circle always contains the number of equations equal to the number of unknowns. But if there are sections formed solely by the ideal sources of current j or contours formed entirely by the ideal sources of the voltage e, then it becomes undefined, since the equations, compiled according to Kirchhoff’s laws for such intersections and contours (further called them EJ-degenerate) do not contain unknowns , although the laws themselves must be strictly adhered to.

Similar problems often occur in practice: enough to call the three-phase circle, the ideal voltage sources of which are connected by a triangle, or ideal sources of current — in the star. But most often EJ- degeneration arises in the tasks of analysis of radio-electronic circles.

Scientific research often encounters practical problems whose solutions are simplified too much under the conditions of one or another local idealization, or even impossible without it. Therefore, one must be responsible to analyze the results obtained in each case. The problems of singularity were considered only in the sense of exacerbating the problem. Any mathematical image of a real physical process is carried out under one or another logical assumptions, including idealization. But idealization should use the discretion of .