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The Motion of a Bead Sliding on a Wire in Fractional Sense

100%

Baleanu D., Jajarmi A., Asad J., Blaszczyk T.

Acta Physica Polonica A

2017

vol. 131

issue 6

1561-1564

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.

An action for a classical string, the equation of motion and group invariant classical solutions

88%

Bracken P.

Open Physics

2008

vol. 6

issue 3

662-670

A string action which is essentially a Willmore functional is presented and studied. This action determines the physics of a surface in Euclidean three space which can be used to model classical string configurations. By varying this action an equation of motion for the mean curvature of the surface is obtained which is shown to govern certain classical string configurations. Several classes of classical solutions for this equation are discussed from the symmetry group point of view and an application is presented.

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1 Acta Physica Polonica A

1 Open Physics

1 2017

1 2008

1 Asad J.

1 Baleanu D.

1 Blaszczyk T.

1 Bracken P.

1 Jajarmi A.

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The Motion of a Bead Sliding on a Wire in Fractional Sense

An action for a classical string, the equation of motion and group invariant classical solutions