Skip to main content
  • 522 Accesses

Abstract

In this chapter, we provide some mathematical preliminaries, useful technical lemmas.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. H. Goldstein, Classical Mechanics (Addison-Wesley, Massachusetts, 1951)

    MATH  Google Scholar 

  2. L. Meirovitch, Analytical Methods in Vibration (Macmillan, New York, 1967)

    MATH  Google Scholar 

  3. C.D. Rahn, Mechatronic Control of Distributed Noise and Vibration (Springer, New York, 2001)

    Book  Google Scholar 

  4. N.S. Abhyankar, E.K. Hall, S.V. Hanagud, Chaotic vibrations of beams: numerical solution of partial differential equations. J. Appl. Mech. 60, 167–174 (1993)

    Article  MathSciNet  Google Scholar 

  5. A.P. Tzes, S. Yurkovich, F.D. Langer, A method for solution of the Euler-Bernoulli beam equation in flexible-link robotic systems, in IEEE International Conference on Systems Engineering, 1989, pp. 557–560

    Google Scholar 

  6. A. Tzes, S. Yurkovich, A method for solution of the Euler-Bernoulli beam equation in flexible-link robotic systems, Technical Report CRL-1039-Sp89-R, The Ohio State University, Control Research Laboratory, 1989

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jinkun Liu .

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Tsinghua University Press, Beijing and Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Liu, J., He, W. (2018). Mathematical Preliminaries. In: Distributed Parameter Modeling and Boundary Control of Flexible Manipulators. Springer, Singapore. https://doi.org/10.1007/978-981-10-8300-6_2

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-8300-6_2

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-8299-3

  • Online ISBN: 978-981-10-8300-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics