Please "explain" angular momentum.... BUT!!
I am able to justify how the cross product between the postition from an axis and the velocity of a particle, provides "angular velocity." Such an operation maintains "information" about the instantaneous axis of rotation, the magnitudes of the perpedicular disance from the axis and the velocity and mass.
I also know that we can obtain the same result by taking the position vector, converting its components into a skew symmetric matrix and multiplying that matrix by the linear momentum vector.
What I am UNABLE to do (and the reason I solicit guidance) is to explain how a skew symmetric matrix of position components times the momentum vector gives the angular momentum.
In other words, it seems I am still tied to the cross product.
How can I "explain" the meaning of the angular momentum WITHOUT resorting to the cross product and going DIRECTLY to the skew symmetric form?