2 ms·

There could be some dynamics I'm overlooking that make your theory work. Normally with a resonant system, energy essentially gets added near the resonant freque

There could be some dynamics I'm overlooking that make your theory work. Normally with a resonant system, energy essentially gets added near the resonant frequency and it acts as a bandpass filter for everything else, so my guess is it's only the first harmonic of whatever jerking motion you try that's actually contributing energy. As I say, that's really for a simple oscillator, there may be something about the swing system that gives it an impulse response that matches what you are describing. Edit: I wonder if the abrupt change is better simply because it lets a person maximize the amplitude of the push they give, so more energy goes in at the first harmonic anyway. That's probably the explanation.

amluto 3y ago
But the process isn’t energy-limited — it’s displacement limited. Your arms have a certain length, your body has a certain mass distribution, and you can force the angle by a certain amount. So, if you want a heuristic, integrate pumping displacement times swing position, where the pumping displacement has a fixed maximum. The result is maximized by a square wave.
avar 3y ago
Isn't the flaw that the posted model assumes that you're essentially bolted to the swing by your ass, and only able to move your legs and upper body, excluding the arms? Whereas an actual person on a swing has two points of contact along the pendulum: where they sit, but also the point at where their arms are grabbing the rope (or "rod", in this model). I think what the GP is talking about is a technique where you essentially perform a partial pull-up near the top of the arch.
- amluto 3y ago
  I think m_1 is roughly your butt, and m_3 is roughly your shoulders. Phi is the angle your body makes wrt the chain. So pulling on the chain changes phi. I think the idea is that three masses can model a center of mass that may not coincide with the butt as well as moment of inertia — mass, moment of inertia and CM displacement is three parameters, and three point masses gives enough degrees of freedom. But three point masses cannot model non-rigid-body effects. The offset of CM from butt can vary (by bending one’s knees if nothing else), the CM offset from the swing can vary in two dimensions. I don’t know how much this matters.
thsksbd 3y ago
A swing (pendulum generally) isn't a harmonic oscillator, except in the limit of small angle. But to your point, that just means the user (subconsciously) adjusts the frequency.

amluto 3y ago

But the process isn’t energy-limited — it’s displacement limited. Your arms have a certain length, your body has a certain mass distribution, and you can force the angle by a certain amount. So, if you want a heuristic, integrate pumping displacement times swing position, where the pumping displacement has a fixed maximum. The result is maximized by a square wave.

avar 3y ago

Isn't the flaw that the posted model assumes that you're essentially bolted to the swing by your ass, and only able to move your legs and upper body, excluding the arms? Whereas an actual person on a swing has two points of contact along the pendulum: where they sit, but also the point at where their arms are grabbing the rope (or "rod", in this model). I think what the GP is talking about is a technique where you essentially perform a partial pull-up near the top of the arch.

amluto 3y ago
I think m_1 is roughly your butt, and m_3 is roughly your shoulders. Phi is the angle your body makes wrt the chain. So pulling on the chain changes phi. I think the idea is that three masses can model a center of mass that may not coincide with the butt as well as moment of inertia — mass, moment of inertia and CM displacement is three parameters, and three point masses gives enough degrees of freedom. But three point masses cannot model non-rigid-body effects. The offset of CM from butt can vary (by bending one’s knees if nothing else), the CM offset from the swing can vary in two dimensions. I don’t know how much this matters.

thsksbd 3y ago

A swing (pendulum generally) isn't a harmonic oscillator, except in the limit of small angle. But to your point, that just means the user (subconsciously) adjusts the frequency.