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Originally Posted by Rivkin
... My problem is that for example it's hard for me to understand why the center of gravity is going to be a node for all waves (it should not be for at least for the waves with an odd number of halfwavelengths).
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The center of gravity is a balance point and the centers of inertia and percussion are located at different points along the blade. The respective centers are features of the weight distribution and mechanical properties of the sword (which mostly comprises the blade and the tang).
Waves do not originate from any of these centers. Waves are set up at the point of impact and spread out from that point. The further away the point of impact is from the vibrational node, then the more vibration will be transmitted along the blade and will be felt in the handle.
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Originally Posted by Rivkin
... Concerning the hilt, it seems more like a boundary condition to me, rather than a center of gravity. Concerning longer swords having higher frequencies and wider diaposon, it seems counter-intuitive to me - I would expect smaller swords to have larger frequencies and bigger separation in between of individual modes, but that's just my guess.
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The tang is continuous with the blade and would not be a boundary condition. Depending on the properties of the handle covering materials there may be some dampening of the vibration transmitted from the tang to the hand. My colleagues assure me that physics dictates that the longer the blade, the longer the sweet spot and the higher the frequency of vibrations.
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Originally Posted by Rivkin
... Concerning the sliding mass question, again, what are the possible benefits of this construction vs. simply high momentum fixed mass weapon - nothing simple comes to mind.
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I cannot see any real benefits to a sliding mass. That was the conclusion of my esteemed colleagues also -- they are skeptical that any greater force could be achieved, and the sliding mass would introduce unpredictable and inconsistent properties of the sword depending on how it was wielded.
Ian.