Principle of Minimal Energy effect

Abstract

nowadays, it is familiar to designers to use a numerical method for design, optimization or verification of technical device parameters. The well-known software resources are built on principles of finite or boundary elements (or finite differences several years ago). These methods (especially the Finite Element Method -FEM) have been built on common basic principles; the most important is the Principle of Minimal Energy (described eg by R. P. Feynman in 1966).The basic ideas of the Principle of Minimal Energy will be presented in the paper, followed by practical examples. The reader will be able to follow the principle and build an understandable theory on professional numerical methods basics, theirs possible advantages and disadvantages and shortcomings. The main idea presented in the paper is based on very simple example -motion in the gravitational field of the earth.

Application of Minimum Energy Effect to Numerical Reconstruction of Insolation Curves

“…The course of the effect of energies depending on the value at point C is a simple task that can be performed by virtually any mathematical apparatus. In [37], the authors of the article proved that a MEE system really tends to reconstruct the original curve and thus set the value of the approximation in accordance with reality. Linear interpolation, of course, introduces considerable inaccuracy into the system-this manifests itself (see Section 5) in a significantly different value of the energy effect compared to the original curve.…”

“…According to [36], an important element is the effect S of the differential energy W diff in the time interval from t 1 (start time of the event) to t 2 (end time of the event) [37]:…”

“…A detailed analysis of the characteristic properties of the Method is presented in [37]. The situation is illustrated in Figure 1, where three points are defined:…”

“…1 Through a detailed analysis of the described event, the authors concluded in [37] that the method of Minimum Energy Effect tends to reconstruct the value of the original quantity at the selected point. This means that when moving point C up or down, the value of the energy effect is always higher than it would be if the height of point C was set to the original (blue) curve.…”