Actually -- there is. Humans are a multiple inverted pendulum -- and you stabilize a multiple inverted pendulum by bouncing it vertically from the support at a certain range of frequencies of simple harmonic oscillation (can we spell -- "furitama
"?). See here for a triple- pendulum, stably inverted
-- stability of this system requires no feedback control whatsoever -- just the pure physics of motion. The stability parameters (frequency range etc.) are given by a diffy-q Mathieu function
Walking is just moving the pendulum from one support to the other
in an alternating series (a second oscillation -- at right angles to the first) -- which now makes it complex harmonic oscillation -- and thus a potentially chaotic system -- in the technical sense.
Actually, no. In fact, the reference you cited disproves your whole argument. Let me quote:
"Other considerations, however, reveal limitations to the pendulum model. It successfully explains differences in energy exchange between walking and running, but it does not quantitatively explain how they should vary as a function of walking speed. For example, as speed increases, there are changes in the kinetic and gravitational potential energy exchange34 and the stance leg appears to behave less like a pendulum, but the pendulum analogy does not explain why this is the case. It gives no reason why longer and faster steps (up to the theoretical maximum walking speed) should require a different amount of mechanical work and force than shorter and slower steps. Taken literally, pendulum mechanics predict that a step requires no work or force whatsoever.17 Once walking has commenced, there is no reason why work must be performed to maintain the conservative motion. The pendulum analogy also does not apply to double-limb support, where a pendulum (inverted or otherwise) clearly cannot swing. Although the pendulum analogy is important for understanding how walking can be economical, it does not explain why walking costs energy at all. In that respect, the inverted pendulum model is incomplete.
Your whole inverted pendulum model falls apart at just a cursory glance. As soon as you look at it in a complex model, especially the human body ... well, you have a better chance at winning the Powerball Lottery ... twice in a row.
Do you really want to get into "simple harmonic oscillation", which by its definition has no real forces acting on it? For example, "In real oscillators, friction, or damping, slows the motion of the system. Due to frictional force, the velocity decreases proportional to the acting frictional force. Whereas Simple harmonic motion oscillates with only the restoring force acting on the system, Damped Harmonic motion experiences friction." You are basing your theory on a simple model that is used in unrealistic conditions, let alone based upon the human model. Your "simple harmonic oscillation" falls apart at just a cursory glance.
All props to the IS/IP crowd for what they work on doing within it -- this is the sandbox of stability that they play in. The physics says so.
The oscillatory component dynamic or (what is missed by those who resist the physics on this point) its physical equivalent in potentials -- formed by poising moments within the body ) -- is the inherent basis for aiki manipulation of stability. The physics AND Ueshiba said so
No, the physics doesn't say so. Your models have never shown any basis in the theoretical world for working, let alone the complex, real world of the human body.
AND THEN, when someone actually does gain the required knowledge (and wins a Nobel prize for it) of how the human body functions in relation to the physics world, that will only determine the majority of people, not those rare, unique martial artists who have IP/aiki. All real world tests to this date have shown that these people's body functions entirely differently than normal people.
And no, Ueshiba didn't say so. Current literal translations show that Ueshiba stated and restated ancient martial training theories in regards to IP/aiki.
But, all this is off topic. Please start a different thread if you want to continue trying to use physics in regards to aikido.