Re: [eigen] Eigen and rigid body simulation

[Mathieu Gautier <mathieu.gautier@xxxxxx>]

> I was confused that you called these functions log() and exp()

yes, it's a little bit tricky because there's two different exponential 
function, and both have a mathematical definition.

1/ the exponential of quaternion generalize the exponential of complex 
number to quaternion. This exponential is actually useless for rigid 
body motion.

2/ the exponential of an element of the Lie algebra so(3) (Angular 
Velocity) return an element of the Lie group SO(3) which are in fact the 
rotation matrices.
This exponential function is defined by the sum of 1/k! A^k with k in 
[0; infinity[ where A is in SO(3). This exponential links a rotation and 
 the angular velocity.

The main problem is that we choose to represent a rotation with a 
quaternion. It's very usefull, but have some drawbacks. For example, 
adding two quaternions have no meanings when these quaternion represents 
 rotation. That's why I introduce a Rotation3D to reflects this 
distinction.
I don't know if it's better to have a class Quaternion to represents the 
classical quaternion and another class to represents 3D rotation with a 
link (inheritance, ownership) to this Quaternion class.

--
Mathieu