Rigid Body Kinematics

Linearity

Summary

This video leads students through describing the motion of all points on a wobbly disk as a function of time. Properties of time independent rotation matrices are explored. The problem of the wobbly disk is scaffolded through a sequence of increasingly more complicated motions.

Learning Objectives

After watching this video students will be able to:

Identify rotation matrices.
Decompose the motion of the wobbly, thrown disk into translational and rotational components.
Write the rotational motion of the disk as a product of rotation matrices.

Funding provided by the Singapore University of Technology and Design (SUTD)

Developed by the Teaching and Learning Laboratory (TLL) at MIT for SUTD

It is highly recommended that the video is paused when prompted so that students are able to attempt the activities on their own and then check their solutions against the video.

During the video, students will:

Identify the eigenvalues and eigenvectors of rotation matrices.
Explain what complex eigenvalues mean in terms of a geometric transformation of a vector space.
Determine whether all orthonormal matrices describe rotational transformations.
Write matrices describing rotational components of a real-world, rigid body motion.
Find an expression for a complex rigid body, rotational, time-dependent motion in terms of combinations of simple rotations about standard basis vectors.