Site is still under construction. Math is still under review.
Gravity exists only if checked.
Motor power is preset and is active if checked.
Damping is preset and is active if checked-otherwise, it is zero.
At the specified time, Motor is turned off AND GRAVITY IS ACTIVATED (meaning, the a restraining pin is pulled)
Plots report total, kinetic and potential energy. Potential Energy is 0 when the pendulum is horizontal
Abstract
This project researches the energy losses or gain by the numerical integration in numerical methods used to integrate the equations of motion obtained using the Moving Frame Method in Dynamics.
This paper deploys a new method in Dynamics, implements a numerical integration scheme, and assesses the change in mechanical energy. This research builds the physical hardware and compares the theory and experiment using 3D software. It demonstrates that this new method is eminently accessible by undergraduate students.
The Moving Frame Method (MFM) is a new method in dynamics. It is founded on Lie Group Theory to model rotations of objects, Cartan’s moving frames to model the change of a frame in terms of the frame, and a new notation from the discipline of geometrical physics. The MFM presents a notation for single bodies, linked systems and robotics in which the notation is consistent.
This research uses the MFM to extract the equations of motion of a linked system. This paper demonstrates the power of the MFM and a selected numerical integration scheme to assess how the mechanical energy is changed during the implementation.
The equations are supplemented with models of energy loss at the bearings.
The equations of motion are structured on the Special Euclidean Group. The Principle of Virtual work, supplemented with a restriction on the virtual angular velocities
This paper implements the Newmark Beta Method to solve the equations for a specific two-link structure.
The authors built the structure to observe the actual motion and approximate the energy loss functions.
Web Graphics Library (WebGL) is a JavaScript API for rendering interactive 2D and 3D graphics within any compatible web browser without the use of plug-ins. This project demonstrates the power of WebGL and the ease with which one can supplement analysis with visualization.