Publication details
Variační počet - přirozený aparát fyziky
| Title in English | Calculus of variations - a natural tool of physics |
|---|---|
| Authors | |
| Year of publication | 2015 |
| Type | Article in Periodical |
| Magazine / Source | Československý časopis pro fyziku |
| MU Faculty or unit | |
| Citation | |
| Field | Theoretical physics |
| Keywords | calculus of variations; geometry; physics; first order problems; inverse problem; variational forces |
| Description | It is said that one of characteristic features of physical theories is their beauty. Having in mind the “mathematical aesthetic appearance” one can state that the calculus of variations highly fulfils this requirement. It is also well known that correct physical theories (those verified experimentally), are often variational, i.e. based on a variational principle: classical mechanics, relativistic mechanics, quantum mechanics, classical electrodynamics, … We present on a very basic level the fundamental ideas and classical approaches of the calculus of variations, including examples of their use in geometry and physics. We focus on the first order variational principle, emphasizing mechanics, because, contrary to field theories, the variational problems in mechanics depend on one independent variable only (usually time in physics). |