Taking the hint from usual parametrization of circle and hyperbola, and inspired by the pathwork initiated by Cayley and Dixon for the parametrization of the “Fermat” elliptic curve x3+ y3= 1 , we develop an axiomatic study of what we call “Keplerian maps”, that is, functions m(κ) mapping a real interval to a planar curve, whose variable κ measures twice the signed area swept out by the O-ray when moving from 0 to κ. Then, given a characterization of k-curves, the images of such maps, we show how to recover the k-map of a given parametric or algebraic k-curve, by means of suitable differential problems.

Gambini A., Nicoletti G., Ritelli D. (2021). Keplerian trigonometry. MONATSHEFTE FÜR MATHEMATIK, 195(1), 55-72 [10.1007/s00605-021-01512-0].

Keplerian trigonometry

Gambini A.;Nicoletti G.;Ritelli D.
2021

Abstract

Taking the hint from usual parametrization of circle and hyperbola, and inspired by the pathwork initiated by Cayley and Dixon for the parametrization of the “Fermat” elliptic curve x3+ y3= 1 , we develop an axiomatic study of what we call “Keplerian maps”, that is, functions m(κ) mapping a real interval to a planar curve, whose variable κ measures twice the signed area swept out by the O-ray when moving from 0 to κ. Then, given a characterization of k-curves, the images of such maps, we show how to recover the k-map of a given parametric or algebraic k-curve, by means of suitable differential problems.
2021
Gambini A., Nicoletti G., Ritelli D. (2021). Keplerian trigonometry. MONATSHEFTE FÜR MATHEMATIK, 195(1), 55-72 [10.1007/s00605-021-01512-0].
Gambini A.; Nicoletti G.; Ritelli D.
File in questo prodotto:
File Dimensione Formato  
Gambini2021_Article_KeplerianTrigonometry.pdf

accesso aperto

Tipo: Versione (PDF) editoriale
Licenza: Licenza per Accesso Aperto. Creative Commons Attribuzione (CCBY)
Dimensione 446 kB
Formato Adobe PDF
446 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/829255
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact