Skip to main content
SpringerLink
Log in

A New Expression for Higher Order Accelerations and Poles Under the One Parameter Planar Hyperbolic Homothetic Motions

  • Published:
Advances in Applied Clifford Algebras Aims and scope Submit manuscript

Abstract

The one parameter planar hyperbolic homothetic motion was introduced in Ersoy and Akyigit (Adv Appl Clifford Algebras 21:297–313, 2011). We give a formula for higher order accelerations and poles under this motion. In the case of the homothetic rate \({h\equiv 1}\) we obtain the higher order accelerations and poles under one parameter planar hyperbolic motion which was given by Sahin and Yüce (Math Probl Eng 2014, 2014). Also, the higher order velocities and accelerations are analyzed by taking the angle of the rotation instead of the parameter of the motion.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Blaschke, W.; Müller, H.R.: Ebene Kinematik. Verlag Oldenbourg, Mnchen (1956)

  2. Ersoy S., Akyigit M.: One-parameter homothetic motion in the hyperbolic plane and Euler–Savary formula. Adv. Appl. Clifford Algebras 21, 297–313 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Fjelstad P.: Extending special relativity via the perplex numbers. Am. J. Phys. 54, 416422 (1986)

    Article  MathSciNet  Google Scholar 

  4. Motter A.E., Rosa M.A.F.: Hyperbolic calculus. Adv. Appl. Clifford Algebras 8, 109 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  5. Sahin, S.; Yüce, S.: Higher order accelarations and poles under the one parameter planar hyperbolic motions and their inverse motions. Math. Probl. Eng., 2014 (2014)

  6. Sobczyk G.: The hyperbolic number plane. Coll. Math. J. 26, 268 (1995)

    Article  MathSciNet  Google Scholar 

  7. Ulrych S.: Representations of Clifford algebras with hyperbolic numbers. Adv. Appl. Clifford Algebras 18, 93–114 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Yaglom I.M.: A Simple Non-Euclidean Geometry and its Physical Basis. Springer, New York (1979)

    MATH  Google Scholar 

  9. Yaglom I.M.: Complex Numbers in Geometry. Academic Press, New York (1968)

    MATH  Google Scholar 

  10. Yüce S., Kuruoglu N.: Holditch-type theorems fort he planar Lorentzian motons. Int. J. Pure Appl. Math. 17, 467–471 (2004)

    MathSciNet  MATH  Google Scholar 

  11. Yüce S., Kuruolu N.: Holditch theorem and Steiner formula for the planar hyperbolic motions. Adv. Appl. Clifford Algebras 20, 195–200 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Yüce S., Kuruoglu N.: one-parameter plane hyperbolic Motions. Adv. Appl. Clifford Algebras 18(2), 279–285 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Sciences, Yildiz Technical University, Esenler, 34210, İstanbul, Turkey

    Serdal Şahin & Salim Yüce

Authors
  1. Serdal Şahin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Salim Yüce
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Serdal Şahin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Şahin, S., Yüce, S. A New Expression for Higher Order Accelerations and Poles Under the One Parameter Planar Hyperbolic Homothetic Motions. Adv. Appl. Clifford Algebras 26, 1061–1068 (2016). https://doi.org/10.1007/s00006-015-0569-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00006-015-0569-2

Mathematics Subject Classification

Keywords

Search

Navigation