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Online Resource on Rotations with Rigid Body Dynamics Applications

oliver oreilly's picture

Dear Colleague,

The online resource on rotations,

 http://rotations.berkeley.edu

has been operational now for nearly 7 years and has been recently updated with material from the literature. Among the latest additions, we note the following subjects:

  1. A discussion of geodesics of SO(3). While in their simplest realization, these rotations correspond to constant angular velocity motions the temporal behaviors of the axis and angle of rotation can be complex. Moreover, the rotations correspond to great circles on a three sphere, curves on Steiner’s roman surface, and have application to optometry.
  2. The discussion of singularities in sets of Euler angles has been updated and corrected. A discussion of the distinction between Euler angle singularities and gimbal lock and why they are not identical has now been included. This material is based on a recent paper
  3.  Simulations of the t-handle in space (also known as the Dzhanibekov effect or the twisting tennis racket) that demonstrates the instability of a steady rotation of a rigid body about its intermediate axis of inertia have been included.
  4. If you are teaching a course on vehicle dynamics, navigation, robotics, or rotations you might be interested in exploiting the fact that your students' smartphones are equipped with inertial navigation units (IMUs). Daniel Kawano and Prithvi Akella have harnessed the data from the IMU using the Matlab mobile app and used this data to determine the motion of a smart phoneThe codes can also be used when a smartphone is strapped to a vehicle or droid to track the motion of the vehicle or droid.
  5. Material on navigation and motion tracking including an example of the motion of a human head during a vehicle collision is discussed.
  6. Several simulations of tops, including the Poisson top with dynamic friction, simulations of Euler's disk, and the planar double pendulum. 

The newer examples on the site use Matlab’s symbolic toolbox to automatically generate the equations of motion and may be of interest to instructors for advanced engineering dynamics classes. 

On behalf of my coeditors, Alyssa Novelia, Daniel Kawano and Brian Muldoon, we hope the site is helpful to the community and welcome adding references to recent works on rotations.

Sincerely,

Oliver O'Reilly

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