Matrix differentiation(lagrangian dynamics)

[supernova1387]

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

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.

Thanks in advance

 

[lippyka]

.The first term can be differentiated using the chain rule and matrix calculus, which states that if A is a matrix and x is a vector, then:d(x^T A x) = (A + A^T) dxTherefore, we get:dH/dq = 0.5 * (D + D^T) * dq