Gauss principle of minimum constraint

[ndujar]

Hi all.

I am preparing my Phd on Structural Dynamics, and doing some review on the very guts of the variational principles of mechanics.

The thing is I have come into this paper:

http://www.google.es/url?sa=t&source=we ... O1EecXzCnw

And I have found it extremely interesting, since this relatively new formulation claims to solve nearly half of the numerical problems at the relatively low price of just implementing a pseudoinverse calculator...

It is called the Udwadia-Kalaba formulation, and is an application of the Least Constraint Principle enunciated by Gauss.
Theoretically, in terms of physics, it is more or less the same, only that we get accelerations explicitly.
Advantages are numerical.
Instead of having to solve the Lagrangians and, when applicable, the LCPs, they propose to utilize the special properties of the mass matrix and the Penrose pseudoinverse to get the accelerations.
To get this, only ordinary differential equations have to be solved, no Differencial-Algebraic Equations which are so complicated.

What are your opinions?
How easy would it be to prepare Bullet to use it?
Is it worth the effort?

Thank you very much for your feedback

[raigan2]

I'm also quite interested in hearing about this, having just come across: http://research.vuse.vanderbilt.edu/cim ... lished.pdf

However, unless there is an iterative method for calculating the pseudoinverse -- and so far everyone seems to refer to e.g SVD or similarly "big matrix" approaches -- then it doesn't seem that attractive.

I'd love to hear what more knowledgeable people think though

[ndujar]

Hi Raigan:

I have done some further research on this topic. It seems very interesting indeed.
This paper:

http://www.sciencedirect.com/science?_o ... 31e43db7e5

Presents a quite recent application of the method.

To calculate the pseudoinverse, as you point out, they use matlab's pinv (which uses LAPACK, which implements the Singular Value Decomposition).

Nonetheless, they also present a comparison between the "traditional" coordinate partition approach and their Udwadia-Kalaba implementation of the Gauss method. The former takes 1/3rd of the time...so it's really quicker!

Could you please explain me why don't you find it that attractive? I guess it's not for speed reasons...what are the problems involved with the SVD?

I am trying to implement this method and the only negative point I have found is just this, that SVD is an inefficient way to calculate the inverse of a matrix...but in the long run seems to be quicker...and dodges Gauss-Seidel!...wow...

Well thanks!

[Erwin Coumans]

Stephane Redon also wrote some papers discussing Gauss principle of least constraints to solve rigid body constraints.
See http://citeseerx.ist.psu.edu/viewdoc/su ... 1.1.3.9171 (paper can be downloaded from the 'cached' icon)

He also discussed it on this forum: http://www.bulletphysics.org/Bullet/php ... =&f=4&t=20

Stephane seems to have implemented it, but his work is not publically available. It would be nice to have some open source implementation of this.
Thanks,
Erwin