- Tytuł:
- The Motion of a Bead Sliding on a Wire in Fractional Sense
- Autorzy:
-
Baleanu, D.
Jajarmi, A.
Asad, J.
Błaszczyk, T. - Powiązania:
- https://bibliotekanauki.pl/articles/1032352.pdf
- Data publikacji:
- 2017-06
- Wydawca:
- Polska Akademia Nauk. Instytut Fizyki PAN
- Tematy:
-
motion of a bead on a wire
Euler-Lagrange equation
fractional derivative
Grünwald-Letnikov approximation - Opis:
- In this study, we consider the motion of a bead sliding on a wire which is bent into a parabola form. We first introduce the classical Lagrangian from the system model under consideration and obtain the classical Euler-Lagrange equation of motion. As the second step, we generalize the classical Lagrangian to the fractional form and derive the fractional Euler-Lagrange equation in terms of the Caputo fractional derivatives. Finally, we provide numerical solution of the latter equation for some fractional orders and initial conditions. The method we used is based on a discretization scheme using a Grünwald-Letnikov approximation for the fractional derivatives. Numerical simulations verify that the proposed approach is efficient and easy to implement.
- Źródło:
-
Acta Physica Polonica A; 2017, 131, 6; 1561-1564
0587-4246
1898-794X - Pojawia się w:
- Acta Physica Polonica A
- Dostawca treści:
- Biblioteka Nauki
Artykuł