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 supernova1387 Feb21-12 05:36 PM

Matrix differentiation(lagrangian dynamics)

Suppose we can write the total energy of a system like below in Lagrangian dynamics and generalized coordinates:

http://i43.tinypic.com/2laptux.jpg

where H is total energy, D is the inertia matrix and P is potential energy and q is the generalised coordinate.If we differentiate this, it would become like below. I want to know how. Especially how you differentiate the first term which is in quadratic form and one is transpose of the other. Any textbook which covers these stuff would be helpful too.

http://i43.tinypic.com/ea32g0.jpg