This paper presents an extended formulation of the basic continuation problem for implicitly defined, embedded manifolds in . The formulation is chosen so as to allow for the arbitrary imposition of additional constraints during continuation and the restriction to selective parametrizations of the corresponding higher-codimension solution manifolds. In particular, the formalism is demonstrated to clearly separate between the essential functionality required of core routines in application-oriented continuation packages, on the one hand, and the functionality provided by auxiliary toolboxes that encode classes of continuation problems and user definitions that narrowly focus on a particular problem implementation, on the other hand. Several examples are chosen to illustrate the formalism and its implementation in the recently developed continuation core package COCO and auxiliary toolboxes, including the continuation of families of periodic orbits in a hybrid dynamical system with impacts and friction as well as the detection and constrained continuation of selected degeneracies characteristic of such systems, such as grazing and switching-sliding bifurcations.
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e-mail: danko@illinois.edu
e-mail: f.schilder@mat.dtu.dk
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July 2011
Research Papers
An Extended Continuation Problem for Bifurcation Analysis in the Presence of Constraints
Harry Dankowicz,
Harry Dankowicz
Department of Mechanical Science and Engineering,
e-mail: danko@illinois.edu
University of Illinois at Urbana-Champaign
, Urbana, IL 61801
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Frank Schilder
Frank Schilder
Department of Mathematics,
e-mail: f.schilder@mat.dtu.dk
Technical University of Denmark
, 2800 Kongens Lyngby, Denmark
Search for other works by this author on:
Harry Dankowicz
Department of Mechanical Science and Engineering,
University of Illinois at Urbana-Champaign
, Urbana, IL 61801e-mail: danko@illinois.edu
Frank Schilder
Department of Mathematics,
Technical University of Denmark
, 2800 Kongens Lyngby, Denmarke-mail: f.schilder@mat.dtu.dk
J. Comput. Nonlinear Dynam. Jul 2011, 6(3): 031003 (8 pages)
Published Online: December 15, 2010
Article history
Received:
May 5, 2009
Revised:
August 23, 2010
Online:
December 15, 2010
Published:
December 15, 2010
Citation
Dankowicz, H., and Schilder, F. (December 15, 2010). "An Extended Continuation Problem for Bifurcation Analysis in the Presence of Constraints." ASME. J. Comput. Nonlinear Dynam. July 2011; 6(3): 031003. https://doi.org/10.1115/1.4002684
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