We consider the optimal control problem for null curves in de Sitter 3-space defined by a functional which is linear in the curvature of the trajectory. We show how techniques based on the method of moving frames and exterior differential systems, coupled with the reduction procedure for systems with a Lie group of symmetries, lead to the integration by quadratures of the extremals. Explicit solutions are found in terms of elliptic functions and integrals.
Reduction for constrained variational problems on 3-dimensional null curves / Musso, Emilio; Nicolodi, L.. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - STAMPA. - 47:3(2008), pp. 1399-1414. [10.1137/070686470]
Reduction for constrained variational problems on 3-dimensional null curves
MUSSO, EMILIO;
2008
Abstract
We consider the optimal control problem for null curves in de Sitter 3-space defined by a functional which is linear in the curvature of the trajectory. We show how techniques based on the method of moving frames and exterior differential systems, coupled with the reduction procedure for systems with a Lie group of symmetries, lead to the integration by quadratures of the extremals. Explicit solutions are found in terms of elliptic functions and integrals.File | Dimensione | Formato | |
---|---|---|---|
068647-SICON.pdf
accesso aperto
Tipologia:
2. Post-print / Author's Accepted Manuscript
Licenza:
PUBBLICO - Tutti i diritti riservati
Dimensione
207.98 kB
Formato
Adobe PDF
|
207.98 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
https://hdl.handle.net/11583/1921028
Attenzione
Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo