NDLI: Solutions leaving a codimension- $$\varvec{2}$$ sliding

Content Provider	Springer Nature Link
Author	Guglielmi, Nicola Hairer, Ernst
Copyright Year	2017
Abstract	Piece-wise smooth differential equations (their regularization, numerical integration, and classification of solutions) is the topic of the present work. The behaviour close to one discontinuity surface and also the entering into the intersection of two discontinuity surfaces is well understood. Here, we study the solutions that exit a codimension-2 sliding mode. Some results are expected, others come as a surprise. We are able to explain situations, where difficulties in numerical computations are reported in the recent literature. The analysis is based on asymptotic expansions for singularly perturbed problems and on the study of a time-parameterized two-dimensional dynamical system (hidden dynamics). Various situations are illustrated by examples.
Ending Page	1439
Page Count	13
Starting Page	1427
File Format	PDF
ISSN	0924090X
e-ISSN	1573269X
Journal	Nonlinear Dynamics
Issue Number	2
Volume Number	88
Language	English
Publisher	Springer Netherlands
Publisher Date	2017-01-09
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Asymptotic expansions Stiff equations Implicit equations, differential-algebraic equations Classical Mechanics Singular perturbations Sliding mode (Filippov) solutions Vibration, Dynamical Systems, Control Discontinuous equations Automotive Engineering Piece-wise smooth dynamics Mechanical Engineering Discontinuous differential equations Regularization
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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