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artivis / manif

A small C++11 header-only library for Lie theory.
https://artivis.github.io/manif
MIT License
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Feature request: Cotangent space #263

Open GiulioRomualdi opened 1 year ago

GiulioRomualdi commented 1 year ago

Hi @artivis, we are currently your library in our lab. We see that for each Liegroup, manif exposes the associated tangent space but not the cotangent one. I was wondering if there is a reason why it is not implemented and if there is any possible plan to add it.

cc @riccardogrieco

artivis commented 1 year ago

Hi @GiulioRomualdi, There is no plan to add this at the moment but if you'd like to discuss one we can do so. I guess the first step would be to put together some math doc to clarify the topic and set some solid foundations. cc @joansola

joansola commented 1 year ago

Agree. I never digged into the cotangent space, and I am just reading about it rapidly. I have a few questions:

Given a group, is the cotangent space unique? As it is the tangent space? Or are there many possible cotangent spaces?

If it is unique, I guess we could add all its functionality, as we did with the Tangent. What would this functionality consist of? Any idea of what functions / operators / objects are needed?

And a side question: what do you use the cotangent space for?

Joan

On 17 Feb 2023, at 13:03, Jeremie Deray @.***> wrote:

Hi @GiulioRomualdi https://github.com/GiulioRomualdi, There is no plan to add this at the moment but if you'd like to discuss one we can do so. I guess the first step would be to put together some math doc to clarify the topic and set some solid foundations. cc @joansola https://github.com/joansola — Reply to this email directly, view it on GitHub https://github.com/artivis/manif/issues/263#issuecomment-1434544854, or unsubscribe https://github.com/notifications/unsubscribe-auth/AAS2LPLWPX5CEGITDGOLHR3WX5SKFANCNFSM6AAAAAAU43BJ2M. You are receiving this because you were mentioned.

rebcabin commented 3 months ago

The cotangent space seems essential for control applications, as directional derivatives (cotangent covectors) applied to the potential energy effect d'Alembert's Principle. Please see the right-most terms in Equations 16b and 16c of this paper: https://arxiv.org/abs/1609.02898.