On integration of the differential equation of central motion, I

Eugene Leimanis

Rendiconti del Seminario Matematico della Università di Padova (1982)

  • Volume: 68, page 49-61
  • ISSN: 0041-8994

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Leimanis, Eugene. "On integration of the differential equation of central motion, I." Rendiconti del Seminario Matematico della Università di Padova 68 (1982): 49-61. <http://eudml.org/doc/107881>.

@article{Leimanis1982,
author = {Leimanis, Eugene},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {central motion; integrable by quadrature or reducible to first order differential equation},
language = {eng},
pages = {49-61},
publisher = {Seminario Matematico of the University of Padua},
title = {On integration of the differential equation of central motion, I},
url = {http://eudml.org/doc/107881},
volume = {68},
year = {1982},
}

TY - JOUR
AU - Leimanis, Eugene
TI - On integration of the differential equation of central motion, I
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1982
PB - Seminario Matematico of the University of Padua
VL - 68
SP - 49
EP - 61
LA - eng
KW - central motion; integrable by quadrature or reducible to first order differential equation
UR - http://eudml.org/doc/107881
ER -

References

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  1. [1] N.H. Abel, Oeuvres complètes de Niels Henrik Abel, Nouvelle édition, publiée par L. Sylow et S. Lie, tome II, Christiania (1881), p. 35. Zbl0136.00101
  2. [2] G. Armellini, see [13] Whittaker, p. 81. 
  3. [3] R. Cotes, Harmonia mensurarum, 1722. 
  4. [4] E. Kärger, Untersuchung der Bahn eines Punktes welcher mit der Kraft k/r4 angezogen oder abgestossen wird, Archiv d. Mathematik u. Physik, 58 (1876), pp. 225-277. Zbl07.0569.01JFM07.0569.01
  5. [5] A.M. Legendre, Traité des fonctions elliptiques et des intégrales eulériennes, tome I, Paris, 1825. 
  6. [6] E. Leimanis, Sur l'intégration par quadratures des équations du mouvement du centre de gravité d'un projectile dans un milieu de densité variable, C.R. Acad. Sci. Paris, 224 (1947), pp. 1618-1620. Zbl0029.07906MR21758
  7. [7] E. Leimanis, Sur l'intégration par quadratures des équations du mouvement du centre de gravité d'un projectile dans un milieu de densité et température variables, C.R. Acad. Sci. Paris, 224 (1947), pp. 1752-1754. Zbl0029.07907MR21759
  8. [8] E. Leimanis, The application of infinitesimal transformations to the integration of differential equations of exterior batlistics by quadratures, Proc. Second Canadian Math. Congress, Vancouver, 1949; Univ. of Toronto Press, Toronto, 1951, pp. 206-217. Zbl0045.36702MR43987
  9. [9] W. Macmillan, The motion of a particle attracted towards a fixed center by a force varying as the fifth power of the distance, Amer. J. of Math., 30 (1908), pp. 282-306. Zbl39.0773.02MR1506043JFM39.0773.02
  10. [10] I. Newton, Philosophiae Naturalis Principia Mathematica, London, 1687. Zbl0050.00201
  11. [11] V. Nobile, Sulla integrazione delle equazioni del movimento relativo dei due corpi che si attraggono secondo una legge espressa da una certa particolare funzione della distanza, Giornale di matematiche, 46 (1903), pp. 313-338. Zbl39.0774.01JFM39.0774.01
  12. [12] J. Stader, De orbitis et motibus puncti cuiusdam corporei circa centrum attractivum allis, quam Newtoniana, attractionis tegibus sollicitati, Journ. reine u. angew. Math., 46 (1853), pp. 262-281, 283-327. 
  13. [13] E.T. Whittaker, A Treatise on the Analytical Dynamies of Particles and Rigid Bodies, Cambridge, Univ. Press, 4th edition, 1937. Zbl0091.16406MR992404

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