Wyniki wyszukiwania - BazTech

Ograniczanie wyników

2 Journal of Applied Mathematics and Computational Mechanics

2 2020

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

On the fractional-order dynamics of a double pendulum with a forcing constraint using the nonsingular fractional derivative approach

Rangaig Norodin A., Pido Alvanh Alem G., Pada-Dulpina Caironesa T.

Journal of Applied Mathematics and Computational Mechanics

2020

Vol. 19, nr 2

95-106

In this paper, we presented the fractional-order dynamics of a double pendulum, at a small oscillation, with a non-singular derivative kernel. The equation of motion has been derived from the fractional Lagrangian of the system and the considered fractional Euler-Lagrange equation. The generalized force has also been presented in studying the different cases of force, such as horizontal and vertical forcing. The source term is described by the imposed periodic force, and the memory effect gives an additional damping factor described by the fractional order. The integer and fractional orders of the sample phase diagrams were obtained and presented to visualize the effect of the presented fractional order on the system. Also, since the motion of the system dissipates in the fractional regime, the applied force will drive the system out of equilibrium.

New aspects on the fractional Euler-Lagrange equation with non-singular kernels

Rangaig Norodin A.

Journal of Applied Mathematics and Computational Mechanics

2020

Vol. 19, nr 4

89--100

In this paper, we presented some notes in utilizing the fractional integral counterparts of the fractional derivatives with non-singular kernels on the action-like integral in Lagrangian mechanics. Considering a fractional integral, it may suggest that a dissipative term on the resulting fractional Euler-Lagrange equation can be obtained due to the imposed kernel. However, in the case of nonsingular kernel operators, different aspects of the fractional action-like integral were observed, and corresponding (fractionally-modified) Euler-Lagrange were derived, which imposes new insights on the dynamical system under the fractional regime.