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I'm merely repearing Pacheco and Carranza using Aristotlean physics

Possibly this is an area where Aristotelian physics "break". Making the difference between the rising and falling cuts needs an understanding of energy.

The useful energy of the sword is its terminal kinetic energy. But the energy you have to actively put into it is the kinetic energy plus the variation in potential energy. This variation depends only on the final and initial positions of the sword. When it rises, it gains potential energy, when it falls, it loses potential energy. The kinetic energy depends on speed, squared.

If you do the strikes slowly, the potential energy will be significant, and you'll be able to let the sword fall with very little effort compared to what it takes to rise it. But as you strike faster and faster, the difference will diminish. It's entirely possible that at the speed of a full-power sword blow, the difference is relatively small... Hence the tactical considerations take precedence.

Regards,
I would say that the ability to transfer of energy is what makes a sword blow "strong." It is thus a lot more than the maximal kinetic energy of the sword tip.
The strength of the blow lies in the ability to deliver energy into a bind, or continue a cut. Effectively, preventing energy from "escaping", and transfering potential body energy.

When it comes to rising cuts, the swing itself might be weaker, but if you can get your body behind it, the blow is still quite strong.

But the weapon hand diagonal strike is still the one with the most potential force. If you can get you body behind it. If standing weapon foot forward, your can not do this as effectively as you can by stepping forward in support of a inside blow.
Vincent,

Don't no much about physics but I do know that I like to play a dick sometimes. (Sam Cooke)

The ground reaction force is equal and opposite to gravity (your weight). So, you are forever standing still, since they cancel each other. What do you do to walk? You move your legs. Did you? And how would you do that? You can't, forces are cancelling each other.

A sword has no energy, it's an object. It's the swordsman potential energy that has to be converted to kinetic energy (and into the sword). The admonition to drop your sword is not about dropping it (just open your hands) but about not interfering with the the kinetic energy. If you muscle your sword with your arms it actually slows down and if you look at people cutting upwards they mostly don't muscle it, it is nearly impossible to do that, although there are exceptions.

And Vincent, all this is written 'tongue in cheek'. We are on the internet and there is no appropriate emoticon for those who can't read, and I didn't mean you. See my first line.
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