Classical Physics
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Showing new listings for Thursday, 14 November 2024
- [1] arXiv:2411.08074 [pdf, html, other]
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Title: Precession of the elastic pendulum on the rotating EarthComments: 18 pages 30 figuresSubjects: Classical Physics (physics.class-ph)
We present a numerical solution of the nonlinear differential equation for a pendulum with an elastic string on the rotating Earth, for different values of string stiffness at different geographic latitudes.
- [2] arXiv:2411.08283 [pdf, html, other]
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Title: The surprising subtlety of electrostatic field linesComments: 8 pages, 4 figures; to appear in the American Journal of PhysicsSubjects: Classical Physics (physics.class-ph); Physics Education (physics.ed-ph)
Electric fields are commonly visualized with field line diagrams, which only unambiguously specify the field's direction. We consider two simple questions. First, can one deduce if an electric field is conservative, as required e.g. in electrostatics, from its field lines alone? Second, are there conservative electric fields with straight field lines, besides the familiar textbook examples with spherical, cylindrical, or planar symmetry? We give a self-contained introduction to the differential geometry required to answer these questions, assuming only vector calculus background.
- [3] arXiv:2411.08600 [pdf, html, other]
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Title: Optimal damping adapted to a set of initial conditionsComments: Submitted to Journal of Sound and VibrationSubjects: Classical Physics (physics.class-ph)
Vibrating systems can respond to an infinite number of initial conditions and the overall dynamics of the system can be strongly affected by them. Therefore, it is of practical importance to have methods by which we can determine the damping that is in some sense optimal for all initial conditions, or for a given set of initial conditions. For a single and multi degree of freedom systems, we determine the optimal damping coefficients adapted to different sets of initial conditions using the known method of minimizing the (zero to infinity) time integral of the energy of the system, averaged over a set of initial conditions, and using two new methods that we introduce. One method is based on determining the damping for which the energy of the system, averaged over a set of initial conditions, drops the fastest to a given threshold value. The other method is based on determining the damping that gives minimal average settling time of the system, where we take that the system settled when its energy dropped to a given threshold value. We show that the two new methods give results for optimal damping that are in excellent agreement with each other, but are significantly different from the results given by the minimization of the average energy integral. More precisely, for considered multi degree of freedom systems and sets of initial conditions, the two new methods give optimal damping coefficients that converge to the critical damping of the first mode as the target energy threshold decreases. On the other hand, for these same systems and sets of initial conditions, the method of minimizing the average energy integral gives optimal damping coefficients which are deep in the overdamped regime with respect to the first mode.
New submissions (showing 3 of 3 entries)
- [4] arXiv:2411.08694 (cross-list from nlin.CD) [pdf, html, other]
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Title: Intensity landscapes in elliptical and oval billiards with a circular absorbing regionComments: 8 pages, 9 figures, comments welcomeSubjects: Chaotic Dynamics (nlin.CD); Classical Physics (physics.class-ph)
Billiard models of single particles moving freely in two-dimensional regions enclosed by hard walls, have long provided ideal toy models for the investigation of dynamical systems and chaos. Recently, billiards with (semi-)permeable walls and internal holes have been used to study open systems. Here we introduce a billiard model containing an internal region with partial absorption. The absorption does not change the trajectories, but instead reduces an intensity variable associated with each trajectory. The value of the intensity can be tracked as a function of the initial configuration and the number of reflections from the wall and depicted in intensity landscapes over the Poincaré phase space. This is similar in spirit to escape time diagrams that are often considered in dynamical systems with holes. We analyse the resulting intensity landscapes for three different geometries; a circular, elliptic, and oval billiard, respectively, all with a centrally placed circular absorbing region. The intensity landscapes feature increasingly more complex structures, organised around the sets of points that are a particular number of iteration away from the absorbing region, and enriched by effects arising from multiple absorption events for a given trajectory.
Cross submissions (showing 1 of 1 entries)
- [5] arXiv:2406.04748 (replaced) [pdf, html, other]
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Title: Regular sloshing modes in irregular cavities using metabathymetryComments: 5 pages, 6 figures, abstract presented in Bulletin of the American Physical Society 65 (2020)Subjects: Fluid Dynamics (physics.flu-dyn); Classical Physics (physics.class-ph)
We present a comprehensive investigation, combining numerical simulations and experimental measurements, into the manipulation of water waves and resonance characteristics within closed cavities utilizing anisotropic metamaterials. We engineer the anisotropic media with subwavelength-scale layered bathymetry through the application of coordinate transformation theory and the homogenization technique to a fully three-dimensional linear water wave problem. Experimental and numerical analyses of deformed cavities employing anisotropic metamaterial bathymetry demonstrate regular sloshing mode patterns and eigenfrequencies akin to those observed in rectangular reference cavities with flat bathymetry. Our study underscores the potential of water wave metamaterials in establishing robust anisotropic metabathymetry for the precise control of sloshing modes.
- [6] arXiv:2411.04033 (replaced) [pdf, html, other]
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Title: Energy transport in a free Euler-Bernoulli beam in terms of Schr\"odinger's wave functionComments: 5 pagesSubjects: Mathematical Physics (math-ph); Classical Physics (physics.class-ph); Quantum Physics (quant-ph)
The Schrödinger equation is not frequently used in the framework of the classical mechanics, though historically this equation was derived as a simplified equation, which is equivalent to the classical Germain-Lagrange dynamic plate equation. The question concerning the exact meaning of this equivalence is still discussed in modern literature. In this note, we consider the one-dimensional case, where the Germain-Lagrange equation reduces to the Euler-Bernoulli equation, which is used in the classical theory of a beam. We establish a one-to-one correspondence between the set of all solutions (i.e., wave functions $\psi$) of the 1D time-dependent Schrödinger equation for a free particle with arbitrary complex valued initial data and the set of ordered pairs of quantities (the beam strain and the particle velocity), which characterize solutions $u$ of the beam equation with arbitrary real valued initial data. Thus, the dynamics of a free infinite Euler-Bernoulli beam can be described by the Schrödinger equation for a free particle and vice versa. Finally, we show that for two corresponding solutions $u$ and $\psi$ the mechanical energy density calculated for $u$ propagates in the beam exactly in the same way as the probability density calculated for $\psi$.