Mechanical Hamiltonization of Unreduced ϕ $\phi$ -Simple Chaplygin Systems

IF 2.3 2区 数学 Q1 MATHEMATICS, APPLIED
Alexandre Anahory Simoes, Juan Carlos Marrero, David Martín de Diego
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引用次数: 0

Abstract

In this paper, we prove that the trajectories of unreduced ϕ $\phi$ -simple Chaplygin kinetic systems are reparameterizations of horizontal geodesics with respect to a modified Riemannian metric. Furthermore, our proof is constructive and these Riemannian metrics, which are not unique, are obtained explicitly in interesting examples. We also extend these results to ϕ $\phi$ -simple Chaplygin mechanical systems (not necessarily kinetic).

Abstract Image

未约简φ $\ φ $ -简单Chaplygin系统的机械哈密尔顿化
在本文中,我们证明了未约简φ $\ φ $ -简单Chaplygin动力学系统的轨迹是水平测地线相对于一个修正的黎曼度量的再参数化。此外,我们的证明是建设性的,这些黎曼度量不是唯一的,并在有趣的例子中得到了明确的证明。我们还将这些结果扩展到φ $\phi$ -简单的Chaplygin机械系统(不一定是动力学的)。
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来源期刊
Studies in Applied Mathematics
Studies in Applied Mathematics 数学-应用数学
CiteScore
4.30
自引率
3.70%
发文量
66
审稿时长
>12 weeks
期刊介绍: Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.
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