2born (2born) wrote,

В разделе "Классическая физика" вчера было три симпатичных публикации

Как мы все помним, на этой slinky был в значительной степени построен третий том берклиевского курса физики (Крауфорд "Волны"), причем тогда такие игрушки у нас не продавались, не то что нынче:)

Oscillations of a suspended slinky: https://arxiv.org/abs/2005.12203
Jörg Pretz
This paper discusses the oscillations of a spring (slinky) under its own weight. A discrete model, describing the slinky by N springs and N masses, is introduced and compared to a continuous treatment. One interesting result is that the upper part of the slinky performs a triangular oscillation whereas the bottom part performs an almost harmonic oscillation if the slinky starts with "natural" initial conditions, where the spring is just pulled further down from its rest position under gravity and then released. It is also shown that the period of the oscillation is simply given by T=\sqrt{32L/g}, where L is the length of the slinky under its own weight and g the acceleration of gravity independent of the other properties of the spring.

Очень симпатичное и доступное космологическое:
Cosmic analogues of classic variational problems: https://arxiv.org/abs/2005.12053
Valerio Faraoni
Several classic one-dimensional problems of variational calculus originating in non-relativistic particle mechanics have solutions that are analogues of spatially homogeneous and isotropic universes. They are ruled by an equation which is formally a Friedmann equation for a suitable cosmic fluid. These problems are revisited and their cosmic analogues are pointed out. Some correspond to the main solutions of cosmology, while others are analogous to exotic cosmologies with phantom fluids and finite future singularities.
Comments: 30 pages, 3 figures. Invited paper to appear in Universe

А эти ребята срывают покров тайны с лагранжевого формализма в квантовой теории поля. Но зачем, зачем они внедряют в КТП систему СИ?!?!?!?
Demystifying the Lagrangian formalism for field theories: https://arxiv.org/abs/2005.11393
Gerd Wagner, Matthew W. Guthrie
This paper expands on previous work to derive and motivate the Lagrangian formulation of field theories. In the process, we take three deliberate steps. First, we give the definition of the action and derive Euler-Lagrange equations for field theories. Second, we prove the Euler-Lagrange equations are independent under arbitrary coordinate transformations and motivate that this independence is desirable for field theories in physics. We then use the Lagrangian for Electrodynamics as an example field Lagrangian and prove that the related Euler-Lagrange equations lead to Maxwell's equations.
Subjects: Mathematical Physics (math-ph); Classical Physics (physics.class-ph)
Tags: Мегаучебник или Что я читал и похвалил, маразм, наука, популяризация, разгребая arXiv'ы

  • Post a new comment


    default userpic

    Your reply will be screened

    Your IP address will be recorded 

    When you submit the form an invisible reCAPTCHA check will be performed.
    You must follow the Privacy Policy and Google Terms of use.