2born (2born) wrote,

На случай, если в лагранжевом формализме кому-то что-то кажется непонятным (хотя с чего бы?)...

...вот еще одна методическая статейка:

Demystifying the Lagrangian of classical mechanics: https://arxiv.org/abs/1907.07069

The Lagrangian formulation of classical mechanics is extremely useful for a vast array of physics problems encountered in the undergraduate and graduate physics curriculum. Unfortunately, many treatments of this topic lack explanations of the most basic details that make Lagrangian mechanics so practical. In this paper, we detail the steps taken to arrive at the principle of stationary action, the Euler-Lagrange equations, and the Lagrangian of classical mechanics. These steps are: 1) the calculation of the minimal distance between two points in a plane, to introduce the variational principle and to derive the Euler-Lagrange equation; 2) proving the Euler-Lagrange equations are independent of arbitrary coordinate transformations and motivating that this independence is desirable for classical mechanics; and 3) a straightforward reformulation of Newton's second law in the form of Euler-Lagrange equations and formulation of the principle of stationary action. This paper is targeted toward the advanced undergraduate student who, like our own experiences, struggles with details which are not seen as crucial to the utilization of the tools developed by Lagrangian mechanics, and is especially frustrated by the question ``\textit{why} is the Lagrangian always kinetic minus potential energy?'' We answer this question in a simple and approachable manner.
Tags: Мегаучебник или Что я читал и похвалил, образование, разгребая arXiv'ы

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