Stably placing piecewise smooth objects

1996 ◽  
pp. 149-156
Author(s):  
Chao-Kuei Hung ◽  
Doug Ierardi
Keyword(s):  
Piecewise Smooth ◽  
Smooth Objects

scholarly journals The visual hull of piecewise smooth objects

2008 ◽  
Vol 110 (1) ◽  
pp. 7-18 ◽  
Author(s):  
Andrea Bottino ◽  
Aldo Laurentini
Keyword(s):  
Piecewise Smooth ◽  
Visual Hull ◽  
Smooth Objects

Computing stable poses of piecewise smooth objects

1992 ◽  
Vol 55 (2) ◽  
pp. 109-118 ◽  
Author(s):  
David J. Kriegman
Keyword(s):  
Piecewise Smooth ◽  
Smooth Objects

Approximation properties of repeated de la Vallée-Poussin means for piecewise smooth functions

2017 ◽  
Vol 60 (3) ◽  
pp. 695-713
Author(s):  
I. I. Sharapudinov ◽  
T. I. Sharapudinov ◽  
M. G. Magomed-Kasumov
Keyword(s):  
Piecewise Smooth ◽  
Approximation Properties ◽  
Smooth Functions ◽  
Piecewise Smooth Functions

scholarly journals Discontinuity-induced bifurcations in a piecewise-smooth capsule system with bidirectional drifts

2021 ◽  
pp. 105909
Author(s):  
Bingyong Guo ◽  
Joseph Páez Chávez ◽  
Yang Liu ◽  
Caishan Liu
Keyword(s):  
Piecewise Smooth

Local and global bifurcations in 3D piecewise smooth discontinuous maps

2021 ◽  
Vol 31 (1) ◽  
pp. 013126
Author(s):  
Mahashweta Patra ◽  
Sayan Gupta ◽  
Soumitro Banerjee
Keyword(s):  
Piecewise Smooth ◽  
Global Bifurcations ◽  
Local And Global Bifurcations

scholarly journals Singularly Perturbed Oscillators with Exponential Nonlinearities

2021 ◽  
Author(s):  
S. Jelbart ◽  
K. U. Kristiansen ◽  
P. Szmolyan ◽  
M. Wechselberger
Keyword(s):  
Limit Cycles ◽  
Space Dimension ◽  
Blow Up ◽  
Exponential Convergence ◽  
Model System ◽  
Piecewise Smooth ◽  
Singularly Perturbed ◽  
Model Systems ◽  
Smooth System ◽  
Unique Limit

AbstractSingular exponential nonlinearities of the form $$e^{h(x)\epsilon ^{-1}}$$ e h ( x ) ϵ - 1 with $$\epsilon >0$$ ϵ > 0 small occur in many different applications. These terms have essential singularities for $$\epsilon =0$$ ϵ = 0 leading to very different behaviour depending on the sign of h. In this paper, we consider two prototypical singularly perturbed oscillators with such exponential nonlinearities. We apply a suitable normalization for both systems such that the $$\epsilon \rightarrow 0$$ ϵ → 0 limit is a piecewise smooth system. The convergence to this nonsmooth system is exponential due to the nonlinearities we study. By working on the two model systems we use a blow-up approach to demonstrate that this exponential convergence can be harmless in some cases while in other scenarios it can lead to further degeneracies. For our second model system, we deal with such degeneracies due to exponentially small terms by extending the space dimension, following the approach in Kristiansen (Nonlinearity 30(5): 2138–2184, 2017), and prove—for both systems—existence of (unique) limit cycles by perturbing away from singular cycles having desirable hyperbolicity properties.

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