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SIGEST
SIAM Review ( IF 10.2 ) Pub Date : 2020-10-28 , DOI: 10.1137/20n975129 The Editors
SIAM Review ( IF 10.2 ) Pub Date : 2020-10-28 , DOI: 10.1137/20n975129 The Editors
SIAM Review, Volume 62, Issue 4, Page 867-867, January 2020.
In this section we present “A Stiction Oscillator with Canards: On Piecewise Smooth Nonuniqueness and Its Resolution by Regularizing Using Geometric Singular Perturbation Theory,” by Elena Bossolini, Morten Brøns, and Kristian Uldall Kristiansen. This is the highlighted SIGEST version of an article that first appeared in the SIAM Journal on Applied Dynamical Systems in 2017. The article focuses on a deceptively simple mechanical model: a rigid block moving on a flat surface. The block is attached to a spring and thereby subjected to harmonic forcing, as illustrated in Figure 1. The novelty lies in the fact that the friction between the block and the surface is modeled as stiction, so that the force of friction when the block is sticking can be greater than the force of friction when the block is slipping on the surface. The model takes the form of a discontinuous ODE system that cannot be understood using Filipov's methodology. The authors shed light on nonuniqueness issues arising at the onset of slip, and introduce the notion of regular and singular stiction solutions. To address uniqueness they consider a regularized model and identify a slow manifold that separates sticking and slipping solutions. Some trajectories, in the form of canards, correspond to a delay in the onset of slipping. The work builds on sophisticated ideas from dynamical systems theory, giving clear explanations of many subtle concepts. High quality graphics and computational experiments are used to illustrate the theory. In preparing the SIGEST version, the authors have provided additional references to recent work in this field, notably with respect to blow up of solutions and the use of geometric singular perturbation theory to understand how smooth systems approach nonsmooth ones.
中文翻译：
SIGEST
SIAM评论，第62卷，第4期，第867-867页，2020年1月。
在本节中，我们将介绍Elena Bossolini，MortenBrøns和Kristian Uldall Kristiansen撰写的“带卡角的静力振荡器：关于分段光滑非唯一性及其通过使用几何奇异摄动理论进行正则化解决方案”。这是文章的突出显示SIGEST版本，该文章首次出现在2017年《 SIAM应用动力系统期刊》上。该文章侧重于看似简单的机械模型：在平面上移动的刚性块。如图1所示，将块固定到弹簧上，然后对其施加谐波强迫。新颖之处在于，将块与表面之间的摩擦建模为静摩擦，因此当块为当块在表面上滑动时，粘着力可能大于摩擦力。该模型采用不连续的ODE系统的形式，使用Filipov的方法无法理解。作者阐明了滑动开始时出现的非唯一性问题，并介绍了规则和奇异的粘连解决方案的概念。为了解决唯一性问题，他们考虑使用正则化模型并确定将粘滞和滑移解决方案分开的缓慢流形。鸭绒形式的一些轨迹对应于滑倒开始的延迟。这项工作建立在动力学系统理论的先进思想基础之上，对许多细微的概念进行了清晰的解释。高质量的图形和计算实验用于说明该理论。在准备SIGEST版本时，作者提供了有关该领域最新工作的其他参考，
更新日期：2020-12-05
In this section we present “A Stiction Oscillator with Canards: On Piecewise Smooth Nonuniqueness and Its Resolution by Regularizing Using Geometric Singular Perturbation Theory,” by Elena Bossolini, Morten Brøns, and Kristian Uldall Kristiansen. This is the highlighted SIGEST version of an article that first appeared in the SIAM Journal on Applied Dynamical Systems in 2017. The article focuses on a deceptively simple mechanical model: a rigid block moving on a flat surface. The block is attached to a spring and thereby subjected to harmonic forcing, as illustrated in Figure 1. The novelty lies in the fact that the friction between the block and the surface is modeled as stiction, so that the force of friction when the block is sticking can be greater than the force of friction when the block is slipping on the surface. The model takes the form of a discontinuous ODE system that cannot be understood using Filipov's methodology. The authors shed light on nonuniqueness issues arising at the onset of slip, and introduce the notion of regular and singular stiction solutions. To address uniqueness they consider a regularized model and identify a slow manifold that separates sticking and slipping solutions. Some trajectories, in the form of canards, correspond to a delay in the onset of slipping. The work builds on sophisticated ideas from dynamical systems theory, giving clear explanations of many subtle concepts. High quality graphics and computational experiments are used to illustrate the theory. In preparing the SIGEST version, the authors have provided additional references to recent work in this field, notably with respect to blow up of solutions and the use of geometric singular perturbation theory to understand how smooth systems approach nonsmooth ones.
中文翻译：
SIGEST
SIAM评论，第62卷，第4期，第867-867页，2020年1月。
在本节中，我们将介绍Elena Bossolini，MortenBrøns和Kristian Uldall Kristiansen撰写的“带卡角的静力振荡器：关于分段光滑非唯一性及其通过使用几何奇异摄动理论进行正则化解决方案”。这是文章的突出显示SIGEST版本，该文章首次出现在2017年《 SIAM应用动力系统期刊》上。该文章侧重于看似简单的机械模型：在平面上移动的刚性块。如图1所示，将块固定到弹簧上，然后对其施加谐波强迫。新颖之处在于，将块与表面之间的摩擦建模为静摩擦，因此当块为当块在表面上滑动时，粘着力可能大于摩擦力。该模型采用不连续的ODE系统的形式，使用Filipov的方法无法理解。作者阐明了滑动开始时出现的非唯一性问题，并介绍了规则和奇异的粘连解决方案的概念。为了解决唯一性问题，他们考虑使用正则化模型并确定将粘滞和滑移解决方案分开的缓慢流形。鸭绒形式的一些轨迹对应于滑倒开始的延迟。这项工作建立在动力学系统理论的先进思想基础之上，对许多细微的概念进行了清晰的解释。高质量的图形和计算实验用于说明该理论。在准备SIGEST版本时，作者提供了有关该领域最新工作的其他参考，
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