Physics Asked on January 5, 2021

I was reading in a book that the angular momentum of the $N$-body system is of the form $Q(y,z)=y^TDz$ with $y, z$ vectors and $D$ a matrix. But the angular momentum of the $N$-body system is something like $L=sum_{i=1}^Nq_itimes p_i$ no? How do you put it in the previous form?

**edit :**

I am not sure if this helps but it is the citation that is causing me trouble.

We next consider partitioned Runge-Kutta methods for systems

$dot{y}=f(y,z), dot{z}=g(y,z)$. Usually such methods cannot conserve

general quadratic invariants. We therefore concentrate on quadratic

invariants of the form begin{equation} Q(y,z)=y^TDz end{equation}

where $D$ is a matrix of appropriate dimensions. Observe that the

angular momentum of $N$-body systems is of this form.

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