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

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

引用次数: 0

Abstract

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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平面上谐振子轨道焦点轨迹问题的显式解

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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

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