# Finding the Numerical Solution to a Rigid Body Kinetics Problem

## Summary

This is one of MATLAB Grader problems assigned to engineering sophomores in an introductory dynamics course. This assignment is to solve a system of equation of a rigid body kinetics problem.

## Learning Goals

Students should learn how to represent a system of equations with vectors and solve for numerical solutions. The traditional way to teach dynamics is to let students solve problems by hand, which takes tremendous time. Students don't have enough time to see a variety of problems. With MATLAB Grader assignments, we are able to separate the solving part from setting up equations. This strategy not only saves time but also helps students focus on principle-based equations instead of plugging and chugging to get the results.

There are no other high-order thinking skills developed in this activity as the sole goal of this activity is to introduce students to the Symbolic Math Toolbox.

## Context for Use

The course named Dynamics is for sophomores in four majors including aerospace engineering, civil engineering, mechanical engineering, and engineering physics. Class sizes vary between 25 and 35 students in a private institution.

This is one of MATLAB Grader homework problems assigned three times each week. For students who have followed the schedule to complete the previous assignments, it may only take 10 to 15 minutes to complete. Each assignment will address one skill for using the MATLAB Symbolic Math Toolbox (e.g., how to define symbols or how to take integrals or derivatives). To solve this particular problem, students need to know how to represent vectors and take cross products of vectors, which have been introduced and reinforced in the previous assignments.

Students need to understand how to solve rigid body kinetics problems by applying the Newton's second law and setting up kinematics equations. During the lectures or when they do homework problems, they are only required to set up a system of equations without finding numerical answers as it is very time consuming to find the numerical answers by hand. This type of assignments is to help students understand how to represent a system of equations involving vectors in MATLAB and find the numerical solutions.

The general instructional design principle governing the MATLAB problems is to break down a complete code into small pieces that students can complete within 5-10 minutes. Therefore, we three MATLAB related assignments each week, two are MATLAB Grader problems and one is a computation problem which can be solved either by hand or with MATLAB. Each function (e.g., SYMS, INT or SOLVE) will be introduced and reinforced through at least two or more MATLAB Grader assignments. With such frequent repetition, students could easily achieve mastery without feeling overwhelmed.

## Description and Teaching Materials

This is one of homework assignments. Students are given the equations for solving a rigid body kinetics problem. They are given several lines to complete including defining symbols, converting angles from degrees to radians, representing vectors, and setting up the last vector equation. Students can use pretest to verify their code.

The assignment is attached including the problem statement along with the script. The attachment cannot show the lines for students to complete with different colors like in MATLAB Grader. For your reference, here are the incomplete lines: Lines 7, 12, 16, 19, 24, and 29.

MATLABGraderExampleProblem (Acrobat (PDF) 502kB Sep13 21)

## Teaching Notes and Tips

This assignment cannot be the first assignment for students who never use MATLAB Symbolic Math Toolbox. As mentioned before, students need to know how to represent vectors and do a cross product in addition to setting up a system of equations.

## Assessment

The grade will show whether students have met the goals of the assignment.