## A new publication from the Dr. Haneesh Kesari's group at Brown University:

__Determining rigid body motion from accelerometer data through the square-root of a negative semi-definite tensor, with applications in mild traumatic brain injury__

### in the journal* **Computer Methods in Applied Mechanics and Engineering*

**The highlights of the paper include:**

Algorithm predicts a rigid body’s motion using only four tri-axial accelerometers.

The body’s rotational motion is obtained without time integrating its acceleration.

Algorithm provides the complete kinematics of rigid body motion in the lab frame.

4 tri-axial accelerometers can be in any orientation and any non-coplanar position.

Algorithm will facilitate use of finite element method based brain injury criteria.

Comparison of the predictions from the √AOAO and AOAO algorithms for the acceleration of the material particle 5X5X (see Fig. 4) in the rigid ellipsoid impact simulation (see Section 5.1 for details). Both the √AOAO and AOAO algorithms were fed the same virtual error-inclusive accelerometer data. The data was generated by adding a particular realization of the OU process to the virtual accelerometer data from the rigid ellipsoid impact simulation. The OU realization corresponded to the OU parameter set (μ,σ,β)=(1,10,103)(μ,σ,β)=(1,10,103). Subfigures (a), (b), and (c), respectively, show the comparison for the component of 5X5X’s acceleration in the eiei, i∈Ji∈ℐ, directions. The predictions of the √AOAO algorithm when fed just the virtual accelerometer data, i.e., with no added errors, is also shown in (a), (b), and (c) using black open circles.