Mathematica Notebooks For Classroom Use In Undergraduate Dynamics: Demonstration Of Theory And Examples

The use of the commercially available software package Mathematica, which is capable of both solving equations and visually presenting the results, is described to assist in the teaching of an introductory course in dynamics. Improving instruction within the classroom environment and assisting the students’ learning outside the classroom are goals of this work. The focus of the development presented herein is on the beginning portions of the course, concentrating on mathematical preliminaries and particle dynamics. Mathematica, frequently employed to teach a variety of topics, is used to parallel and illustrate the formal development of equations in a manner consistent with the textbook. Mathematica lends itself to this purpose, as its syntax is not unlike that found in textbooks. The software also allows for user input thus allowing students to vary the parameters defining the problem and to see the variations in the final results. In addition to containing dynamics problems, the Mathematica notebooks also address the more fundamental, but often more abstract, development of critical mathematical relationships. (The term “notebook” refers to a Mathematica file.) For example, some relationships demonstrate the benefits of choosing particular coordinate systems while others help students understand the components used to describe motion along a path by highlighting the intrinsic triad, i.e., the normal, tangential, and binormal unit vectors. The relationships between position, velocity, and acceleration, as well as the effect of taking the derivative of a vector with respect to time are also presented. This paper will discuss our experiences in creating these Mathematica notebooks, will present some examples of notebooks we have created, and will provide advice for instructors wishing to create notebooks of their own. It is hoped these innovative approaches will help educators to better illustrate and will help students to more easily grasp fundamental concepts that are crucial in understanding dynamics.