Abstract Title
Chaotic Toys: Investigative Modeling of a Rotating Spring Pendulum
Additional Funding Sources
The project described was supported by the Ronald E. McNair Post-Baccalaureate Achievement Program through the U.S. Department of Education under Award No. P217A170273. Funding for this project was also supported or partially supported by Idaho State University Office of the Provost Undergraduate Research funds.
Abstract
A rotating elastic spring pendulum is studied to look for the exhibition of rich chaotic behavior and to determine the optimal conditions for striking a domino out of static equilibrium. Given a choice of initial conditions, the nonlinear dynamical system is governed by a system of four dimensionalized 1st order nonlinear ordinary differential equations, all of which are derived through the Lagrangian mechanical framework. A compilation of simulated phase portraits, as well as a three-dimensional computer model, are generated with the aid of the SciPy numerical integration solver primarily for interpretive means and to con irm the mathematical consistency of the equations. Parameters such as angular displacement and spring stiffness are varied on a case-by-case basis to evaluate the qualitative deviations between dissimilar trajectories. These graphical results are used to determine the precise location and time at which the swinging ball would be able to effectively hit the domino.
Chaotic Toys: Investigative Modeling of a Rotating Spring Pendulum
A rotating elastic spring pendulum is studied to look for the exhibition of rich chaotic behavior and to determine the optimal conditions for striking a domino out of static equilibrium. Given a choice of initial conditions, the nonlinear dynamical system is governed by a system of four dimensionalized 1st order nonlinear ordinary differential equations, all of which are derived through the Lagrangian mechanical framework. A compilation of simulated phase portraits, as well as a three-dimensional computer model, are generated with the aid of the SciPy numerical integration solver primarily for interpretive means and to con irm the mathematical consistency of the equations. Parameters such as angular displacement and spring stiffness are varied on a case-by-case basis to evaluate the qualitative deviations between dissimilar trajectories. These graphical results are used to determine the precise location and time at which the swinging ball would be able to effectively hit the domino.
Comments
W10