Dynamics with inequalities : impacts and hard constraints

David E. Stewart

This is the first book that comprehensively addresses dynamics with inequalities. The author develops the theory and application of dynamical systems that incorporate some kind of hard inequality constraint, such as mechanical systems with impact; electrical circuits with diodes (as diodes permit current flow in only one direction); and social and economic systems that involve natural or imposed limits (such as traffic flow, which can never be negative, or inventory, which must be stored within a given facility). Dynamics with Inequalities: Impacts and Hard Constraints demonstrates that hard limits - eschewed in most dynamical models - are natural models for many dynamic phenomena and there are ways of creating differential equations with hard constraints that provide accurate models of many physical, biological and economic systems. The author treats finite- and infinite-dimensional problems in a unified way, so that the theory is applicable to both ordinary differential equations and partial differential equations.

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[目次]

  • Preface
  • 1. Some examples
  • 2. Static problems
  • 3. Formalisms
  • 4. Variations on the theme
  • 5. Index zero and index one
  • 6. Index two: impact problems
  • 7. Fractional index problems
  • 8. Numerical methods
  • Appendix A. Some basics of functional analysis
  • Appendix B. Convex and nonsmooth analysis
  • Appendix C. Differential equations
  • Bibliography
  • Index.

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この本の情報

書名 Dynamics with inequalities : impacts and hard constraints
著作者等 Stewart David E.
出版元 Society for Industrial and Applied Mathematics
刊行年月 c2011
ページ数 xiii, 387 p.
大きさ 26 cm
ISBN 9781611970708
NCID BB06996514
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言語 英語
出版国 アメリカ合衆国
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