Φ-optics and generalized Bianchi–Auerbach equation
Artykuł w czasopiśmie
| Status: | |
| Autorzy: | Cieślak Waldemar, Miernowski Andrzej, Mozgawa Witold |
| Rok wydania: | 2012 |
| Wersja dokumentu: | Elektroniczna |
| Język: | angielski |
| Wolumen/Tom: | 62 |
| Strony: | 2337 - 2345 |
| Web of Science® Times Cited: | 3 |
| Scopus® Cytowania: | 3 |
| Bazy: | Web of Science | Scopus |
| Efekt badań statutowych | NIE |
| Materiał konferencyjny: | NIE |
| Publikacja OA: | NIE |
| Abstrakty: | angielski |
| We consider the family of regular plane closed strictly convex curves and the family of differential equations of special type associated to positive-valued, periodic and continuous functions. Each curve and the solutions of a fixed differential equation determine a family of disjoint closed curves called ϕ-optics. In particular cases we obtain the family of α-isoptics and the family of arc-optic curves. The family of arc-optic curves is closely related to the solutions of the Ulam problem.Wegeneralize the Bianchi–Auerbach equation derived for the problem of floating body to general case of ϕ-optics and we give some of its applications. We present the necessary and sufficient conditions for some geometric quantities connected in a natural way to ϕ-optics to be constant. |
