Re: [eigen] Eigen and rigid body simulation

[Mathieu Gautier <mathieu.gautier@xxxxxx>]

> But when you are talking about linear or angular "mechanics" you should
> also think about its analog applications: thermodynamics and electricity:
>
> The formulas to handle those quantities are exactly the same.
>
> I.e. although most quantites are only 1D (and not 3D like linear and
> angular motion) this is really asking for a generic mechanism to handle
> it.

I agree that there is a strong analogy between these fields (mechanic, 
electric, etc.). But, I think that working in 1D and 3D is too different 
to have a simple unified framework. For example, derivative in cartesian 
space of a rigid motion is not trivial. The point is, with or without a 
unified framework, that mechanical quantities such as velocities, forces 
or rigid motion need their specific representation which reflect the 
space in which they evolve (Lie algebra and Lie group). Moreover the 
basic operation associated to these group can be simplified for the 
specifics group in 3D that's why they need a specific implementation.
> But in either case (only mechanics or generalized) I think it's out of
> the scope of Eigen. It's a good usecase though.

I don't plan to add methods or classes to have a physics(electric, etc.) 
engine in Eigen, I agree that's out of Eigen scope. I just wish to have 
some basic geometric elements handling rigid body motion, like 
quaternion actually reflects rigid body rotation. It's just about 
geometry and not about physics, although the name I used are based on 
mechanical field.

I think that these elements can be usefull for users who wish to use 
Eigen for physics simulation or robotics application, where these kind 
of elements and matrices operation are heavily used.

--
Mathieu