ﻻ يوجد ملخص باللغة العربية
This paper presents a general formulation of equations of motion of a pendulum with n point mass by use of two different methods. The first one is obtained by using Lagrange Mechanics and mathematical induction(inspection), and the second one is derived by defining a vector. Today, these equations can be obtained by employing numerous programs; however, this study gives a very compact form of these equations that is more efficient than solving Euler-Lagrange Equations for every pendulum with more complex structures than simple or double pendulum. Additionally, we investigate what will happen to our n-point mass system when we take limit as number of point masses goes infinity under well-defined assumptions. We find out that it converges to hanging rope system.
The change of the plane of oscillation of a Foucault pendulum is calculated without using equations of motion, the Gauss-Bonnet theorem, parallel transport, or assumptions that are difficult to explain.
The accurate modeling of the dielectric properties of water is crucial for many applications in physics, computational chemistry and molecular biology. This becomes possible in the framework of nonlocal electrostatics, for which we propose a novel fo
The analytical solution of the three--dimensional linear pendulum in a rotating frame of reference is obtained, including Coriolis and centrifugal accelerations, and expressed in terms of initial conditions. This result offers the possibility of trea
In this paper, we explore the stability of an inverted pendulum under a generalized parametric excitation described by a superposition of $N$ cosines with different amplitudes and frequencies, based on a simple stability condition that does not requi
The goal of this paper is to investigate the normal and tangential forces acting at the point of contact between a horizontal surface and a rolling ball actuated by internal point masses moving in the balls frame of reference. The normal force and st