椭圆轨道上变长质心双摆的参数稳定性

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Journal of Geometric Mechanics Pub Date : 2022-01-01 DOI:10.3934/jgm.2021031

José Laudelino de Menezes Neto, G. C. Araujo, Yocelyn Pérez Rothen, C. Vidal

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引用次数: 1

摘要

我们考虑一个平面双摆，它的质心附着在一个椭圆轨道上。我们考虑摆杆的长度随椭圆轨道的半径矢量而变化的情况。我们用哈密顿的观点来看待这个问题，找到了四个线性稳定的平衡位置，并在与摆长和轨道偏心率相关的参数空间中构造了稳定/不稳定区域的边界曲线。

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Parametric stability of a double pendulum with variable length and with its center of mass in an elliptic orbit

We consider the planar double pendulum where its center of mass is attached in an elliptic orbit. We consider the case where the rods of the pendulum have variable length, varying according to the radius vector of the elliptic orbit. We make an Hamiltonian view of the problem, find four linearly stable equilibrium positions and construct the boundary curves of the stability/instability regions in the space of the parameters associated with the pendulum length and the eccentricity of the orbit.

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来源期刊

Journal of Geometric Mechanics MATHEMATICS, APPLIED-PHYSICS, MATHEMATICAL

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Geometric Mechanics (JGM) aims to publish research articles devoted to geometric methods (in a broad sense) in mechanics and control theory, and intends to facilitate interaction between theory and applications. Advances in the following topics are welcomed by the journal: 1. Lagrangian and Hamiltonian mechanics 2. Symplectic and Poisson geometry and their applications to mechanics 3. Geometric and optimal control theory 4. Geometric and variational integration 5. Geometry of stochastic systems 6. Geometric methods in dynamical systems 7. Continuum mechanics 8. Classical field theory 9. Fluid mechanics 10. Infinite-dimensional dynamical systems 11. Quantum mechanics and quantum information theory 12. Applications in physics, technology, engineering and the biological sciences.