[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 549
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Right. Suppose we have something like a sine wave on the input with an amplitude equal to one... It only takes two values of 0 and 1. What would your equation look like?
I don't understand, how can a sine wave take only 2 values?
I'm referring to the model that is described by a linear filter consisting of 2 non-ideal (with decay) harmonic oscillators. The model is quite simple, but remarkable in that, I repeat, for certain values of A and K it gives a response to the Heaviside function 1(t), quite reminiscent of the Elliott wave cycle. Parameters of the model can be identified in real time from quotes, I'm not going to describe it in details - for this you should know at least z-transformation and some suitable method of non-linear optimization, for instance Levenberg-McWardt algorithm is a good choice for MOC. If the model parameters can be identified early enough, then a small part of the remaining cycle can be (attempted) predicted. Which is what I'm doing at the moment.
By the way, the system that appeared a little earlier in this thread, I no longer need it, because firstly it was wrong))), and secondly, I went another way (more successful).
Especially since the parameters that I see in reality, according to the results of numerical calculations, say that the values are exactly as they should be. Which can't help but be pleasing.
I didn't have the guts to go for it... There are too many "buts". But I can do it with my hands.
I once started a thread with a similar picture ;)
May's picture was already there too. I don't want to look for it at all, it's been a long time.
The agitation-arbitrage model of the market. The picture shows the multicurrency interaction after a single equilibrium perturbation.
I didn't have the guts to go for it... There are too many "buts". But I can do it with my hands.
I used this library: kind, and most importantly, professional people wrote everything for us long ago.
So. the force of gravity is applied to the centre of mass.
(2) is the projection onto the axis
(3) -- the transfer (2) to the point of contact with the surface.
(4) -- the projection of (3) onto the vertical axis, balanced by (6) the opposing force of the support
(5) -- projection (3) onto the horizontal axis, balanced by (7) the rest-friction force
(1) -- this is the force that drives the walking motion.
(6) and (7) are simply counteracting forces. Derivatives, eh )))
That's right. But the body has to be brought out of its upright position into this position. And there is only one way to do that - to push off the ground, i.e. to exert force 5 on the ground and get force 7 in response, which moves the centre of mass forward. After that, gravity kicks in and forces us forward so we have to lift the other leg.
We can exclude gravity from consideration altogether - for example, imagine that we are not walking but crawling. All that is left is the force of friction, which has nothing else to do with us. Or swimming - the only force acting on the body in water is the force of viscous resistance.
By the way, why do we fall when we tilt?
In the figure, force 3 (the force of pressure on the surface) is exactly equal to force 2 (the longitudinal component of gravity). F3 = F2 = mg*cos(a). In this case the vertical component of reaction force 6 is bound to be equal to the vertical component of force 3 according to Newton's 3 Law, i.e. F6 = F4 = F3*cos(a). Substituting F3 from the previous one we get: F6 = mg*cos^2(a). It turns out that the support reaction becomes smaller than gravity in modulo when the tilt is at angle a. The resultant force is directed downwards and moves the body in this direction. Well, the horizontal component of the reaction force F7 = mg*sin(a)*cos(a) is not balanced in any way, and so it simply acts on the body until the angle a equals 90 degrees (sin(a)*cos(a)=0), i.e. until the fall.
In full agreement with these calculations, after the fall, the centre of mass of the body is lower and to the left of its original position.