alec-glisman / Swimming-in-Potential-Flow

Study dynamics of inertial active matter in a potential fluid (irrotational, incompressible).
https://doi.org/10.1017/jfm.2022.946
GNU General Public License v3.0
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Review Runge-Kutta 4th order accurate integration for quaternions #8

Closed alec-glisman closed 2 years ago

alec-glisman commented 2 years ago

I recently learned that unit quaternions are not closed under elementwise addition as normal Euclidian vectors are. This implies that time integration of the components is a bit trickier than I first thought.

I need to check how to properly get the unit quaternion "velocity" from "acceleration" and "position" from "velocity" in the second-order integration scheme.

alec-glisman commented 2 years ago

Remember, only the quaternion itself needs to have a unitary norm.

Check the definition of a unit norm again and make sure this is what I am doing in the Udwadia constraint algorithm

It seems that I may also just be able to renormalize the result directly.

alec-glisman commented 2 years ago

Source to look at