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Meccanica

, Volume 46, Issue 2, pp 471–476 | Cite as

Siacci’s resolution of the acceleration vector for a space curve

  • James Casey
Open Access
Brief Note
  • 494 Downloads

Abstract

For motion of a material point along a space curve, a kinematical decomposition, discovered by Siacci, expresses the acceleration vector as the sum of two special oblique components in the osculating plane to the curve. A new proof of Siacci’s theorem is presented.

Keywords

Siacci Space curve Kinematics Classical mechanics Central forces 

References

  1. 1.
    Siacci F (1879) Moto per una linea piana. Atti R Accad Sci Torino 14:750–760 Google Scholar
  2. 2.
    Whittaker ET (1937) A treatise on the analytical dynamics of particles and rigid bodies, 4th edn. Cambridge University Press, Cambridge. Dover, New York (1944) zbMATHGoogle Scholar
  3. 3.
    Grossman N (1996) The sheer joy of celestial mechanics. Birkhäuser, Basel zbMATHCrossRefGoogle Scholar
  4. 4.
    Love AEH (1921) Theoretical mechanics, 3rd edn. Cambridge University Press, Cambridge zbMATHGoogle Scholar
  5. 5.
    Ramsey AS (1933) Dynamics. Cambridge University Press, Cambridge Google Scholar
  6. 6.
    Lamb H (1923) Dynamics, 2nd edn. Cambridge University Press, Cambridge zbMATHGoogle Scholar
  7. 7.
  8. 8.
    Siacci F (1879) Moto per una linea gobba. Atti R Accad Sci Torino 14:946–951 Google Scholar
  9. 9.
    Casey J (2007) Areal velocity and angular momentum for non-planar problems in particle mechanics. Am J Phys 75:677–685 ADSCrossRefGoogle Scholar
  10. 10.
    Guicciardini N (1995) Johann Bernoulli, John Keill and the inverse problem of central forces. Ann Sci 52:537–575 MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of CaliforniaBerkeleyUSA

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