平面上谐振子轨道焦点轨迹问题的显式解

IF 0.5 Q4 PHYSICS, MATHEMATICAL

Journal of Geometry and Symmetry in Physics Pub Date : 2022-01-01 DOI:10.7546/jgsp-64-2022-29-37

Clementina D. Mladenova, Ivaïlo M. Mladenov

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引用次数: 0

摘要

谐振子势在平面上的动态轨道是依赖于实参数的椭圆。前段时间在本刊上，用纯几何方法证明了这些椭圆的焦点轨迹是卡西尼椭圆。这里我们给出了这些显著曲线的几个显式解析参数化。名义上，它们的形式取决于初始距离引力中心的大小和初始速度的大小。我们发现了一些参数化，其中大小和形状的作用可以清楚地区分。

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Explicit Solution of the Focus Locus Problem for the Harmonic Oscillator Orbits in the Plane

Dynamical orbits of the harmonic oscillator potential in the plane are ellipses which depend on a real parameter. Some time ago in this journal it has been proven by purely geometrical methods that the locus of the focuses of these ellipses are Cassinian ovals. Here we present several explicit analytic parameterizations of these remarkable curves. Nominally, their forms depend on the magnitude of the initial distance from the center of attraction and the magnitude of the initial velocity. We have found a few parameterizations in which the roles of the size and shapes can be clearly distinguished.

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来源期刊

Journal of Geometry and Symmetry in Physics PHYSICS, MATHEMATICAL-

CiteScore

1.50

自引率

25.00%

发文量

期刊介绍： The Journal of Geometry and Symmetry in Physics is a fully-refereed, independent international journal. It aims to facilitate the rapid dissemination, at low cost, of original research articles reporting interesting and potentially important ideas, and invited review articles providing background, perspectives, and useful sources of reference material. In addition to such contributions, the journal welcomes extended versions of talks in the area of geometry of classical and quantum systems delivered at the annual conferences on Geometry, Integrability and Quantization in Bulgaria. An overall idea is to provide a forum for an exchange of information, ideas and inspiration and further development of the international collaboration. The potential authors are kindly invited to submit their papers for consideraion in this Journal either to one of the Associate Editors listed below or to someone of the Editors of the Proceedings series whose expertise covers the research topic, and with whom the author can communicate effectively, or directly to the JGSP Editorial Office at the address given below. More details regarding submission of papers can be found by clicking on "Notes for Authors" button above. The publication program foresees four quarterly issues per year of approximately 128 pages each.