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Authors: Abu-Asa'd, Ata
Keywords: Heavy particle
Lagrange equation
Euler-Lagrange equation
Particular solution
Homogenous solution
Numerical solution.
Issue Date: 8-Jul-2019
Publisher: Journal of Theoretical and Applied Mechanics
Citation: Abu-Asa’d, Shanak, & Asad. (2019). CLASSICAL FEATURES OF THE MOTION OF A HEAVY BEAD SLIDING ON A ROTATING WIRE. Journal of Theoretical and Applied Mechanics, 49(Issue 3), 224–232.
Series/Report no.: vol. 49;Issue 3 (2019)
Abstract: In this paper, we study the motion of a heavy bead sliding on a rotating wire. Our first step was constructing the classical Lagrangian of the system. Secondly, we derived the Euler- Lagrange equation (ELE). Thirdly, we solve the obtained ELE, which is a non-homogenous second order linear differential equation. Finally, by using MATLAB the equation is solved numerically for some selected parameters, and for specified initial conditions.
Description: Lagrangian and Hamiltonian mechanics play an important role in solving a wide range of classical physical systems [1–3]. This branch of classical mechanics is based on scalars concepts (i.e. kinetic and potential energies). Classical mechanics books contain many such systems, and for more details one can refer to the three references [1–3] above. Solving such systems by this technique results in obtaining differential equations called equations of motions (i.e. Euler-Lagrange equations). These equations have to be solved for some given initial conditions either analytically or numerically in some cases. In under graduate level mathematician and physician students study an interesting course called ordinary differential equations (ODE). In this course students study techniques that enable them to solve many branches of ODE, see for example [4–7]. Numerical solution of ODE’s are powerful because they help scientists in solving many kinds of DE’s without the need of knowing their analytical solutions due to difficulty, or insufficient data. In literature one can find many numerical methods and techniques that has been considered [8–12]. In this paper, we choose an interesting physical system (a heavy bead sliding in a rotating wire). The importance of this example is due to the fact that the kinetic
ISSN: 1314-8710
Appears in Collections:Applied science faculty

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