Jacobian woes

[Bilbert]

Greetings all,

I have been playing around with some constraint physics programming. During my research, I came across the article "Constrained Dynamics" by Andrew Witkin which really peeked my curiosity. In the article he defined a general constraint equation JWJ^t * l where J is the Jacobian of the constraint vector w.r.t. the force. In other articles, including posts from this site, I encountered similar use of jacobian matrices. A few years ago I took some linear algebra and physics classes, but I have never encountered the use of Jacobian matrices. Researching them on the internet, I understand the definition of such a matrix but I am having trouble finding examples of calculating J from 2 vectors. The code example I downloaded( ODE and bullet ), I can't determine the formula for building these matrices. Would someone please explain howto generate these matrices or perhaps point me in the direction of a good article or book.

Thank much,
Bil

[Dirk Gregorius]

The presentations here explain how to use the Jacobians in the context of rigid body dynamics:

http://www.gphysics.com/files/GDC2007_ErinCatto.zip


A general explanation can be found here:

http://en.wikipedia.org/wiki/Jacobian

[Antonio Martini]

some detailed explanations can be found here:

http://www.cs.ubc.ca/grads/resources/th ... _Cline.pdf
ftp://ftp.diku.dk/diku/image/publicatio ... 050401.pdf

a good book with many examples is Computational Dynamics of A. Shabana.

cheers,
Antonio

[Bilbert]

Thank you. The help is much appreciated.

Bil