

Is there a 4th missing component in the mechanical world? - judegomila
http://www.judegomila.com/2010/11/is-there-4th-missing-component-in.html#heyzap_game=

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kwantam
I've never been convinced that the memristor is worthwhile to consider as a
"fundamental passive device" as everyone seems to want to claim. There are a
few reasons for this:

(1) It's underspecified compared to the fundamental passive circuit elements.
For linear R, L, and C, each has one parameter, its value. Ignoring trivial
cases (viz., resistors), a memristor has as its memristance an arbitrary
function of V and I. As a result, any interesting memristor is automatically
not LTI.

(2) It's not particularly special. Why don't we also define a memcaptor, whose
capacitance is a function of its current history? I could easily do this, for
example, by making a capacitor where one plate is attached by a spring to a
fixed support; then, by adding charge, I move the plate and increase the
capacitance (or, by removing, I decrease it). Oh wait, that's just a nonlinear
capacitor. In the same way, the memristor is just a funny name for a
particular kind of nonlinear resistor.

(3) It's not particularly practical (for the moment). It can't be made in
anything but a very specialized, presumably extremely expensive process. I
hope this changes---I'm sure it'll encourage someone to use them!---but at the
moment this really limits my excitement.

(4) There's nothing I can build with a memristor that I couldn't build
already. This isn't like the invention of the vacuum tube: you give me a
memristance function, and I can build you a pseudo-memristor out of
transistors, Rs, Ls, and Cs. Yes, it could be less {space,power,?} efficient,
but this is not a quantum leap in technology the way the vacuum tube was (one
could not, with 1890s technology, reasonably build something that emulates a
vacuum tube).

I'll admit that strictly interpreting my last argument, the vacuum tube could
be made to emulate a transistor and thus the transistor wouldn't count as a
quantum leap---clearly ridiculous. However, I'd contend that the real value of
the transistor was only evident once it was sufficiently miniaturized and its
production was sufficiently cheap. You show me memristors that are six orders
of magnitude cheaper than transistors and by golly I'll be a convert. Even
then, it'll just be yet another nonlinear device with which we can do
interesting things---and just like the transistor, the memristor will simply
never be as fundamental as R, L, or C.

~~~
sophacles
Regarding your (1), I'm not sure I follow, isn't the fundamental unit of
resistance, ohms, just a function of V and I? Namely V/A. Likewise for
capacitance, the Farad is simply (A/V)s. Basically, your argument feels like
it is begging the question -- we gave those functions of V and I names, so now
they are fundamental units but not the memristor one... because it doesn't
have a name?

~~~
kwantam
No, there's a more intrinsic difference.

Resistor: V = I R

Memristor: V = I M(q)

The memristance is itself a function of the integral of I, and that function
is arbitrary.

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kqr2
Also see _What is the mechanical element equivalent of the memresistor?_

[http://www.quora.com/What-is-the-mechanical-element-
equivale...](http://www.quora.com/What-is-the-mechanical-element-equivalent-
of-the-mem-resistor?q=mechanical+equi)

~~~
judegomila
I sent him an PM. I'm sure there is a lot more to this!

------
judegomila
An inerter is the mechanical equivalent of a capacitor.
<http://www.admin.cam.ac.uk/news/dp/2008081906>

~~~
archgoon
I question whether the article is correct about the "J-Damper" being a
meaningless code-name. In circuit theory, a capacitor can be thought of as a
resistor with purely complex (and frequency varying) impedance. Since "J" is
the standard symbol for the square root of -1, and given the fact that this
device had never been used before, "Imaginary Damper" seems entirely
appropriate.

~~~
davnola
It's actually J for "jounce" <http://www.f1technical.net/features/10586>

------
secretasiandan
Charge being equivalent to position doesn't make much sense to me.

When I learned systems modelling, we studied spring-mass-damper systems right
next to electrical circuits and I have ever since thought of a capacitor as
equivalent to potential energy, an inductor as equivalent to inertia and a
resistor as equivalent to friction.

~~~
colanderman
That's a common view, since force ~ voltage, current ~ velocity (i.e. charge ~
position) seems "intuitively" correct, but it breaks down when you look at
what would be the equivalents of KVL and KCL. KCL states that currents sum to
zero at a node in the absence of capacitance: this is similarly true of forces
(capacitance in this case representing the ability of the node to change
position/"charge").

KVL states that voltage differences sum to zero around a loop: this is
similarly true of velocity differences. This can be difficult to visualize,
but imagine a loop of N springs. Assume the loop can have no net translational
motion (as above, this means it is not capacitive). Now imagine the different
ways each spring can move individually. The loop could rotate as a whole,
meaning half the springs have are moving "up" (i.e. have a positive voltage
across them) and the other half "down" (i.e. have a negative voltage across
them). The loop could be still, but for one element compressing and its
neighbor expanding (i.e. all zero voltages with one positive and one
negative).

The reason the examples in your systems class worked was likely because the
circuits were simple enough that their duals shared the same, or similar,
network structure. You can see this with a purely electrical circuit --
analyze a simple LCR loop, and then swap the L & C equations and you should
get the same result. This breaks down for larger circuits, where you must find
the dual network in addition to swapping Ls and Cs.

~~~
secretasiandan
The invetor's slides say that the only time the analogy breaks down is with
ungrounded capacitors, though its unclear to me what exactly that means (I
don't really feel like thinking too hard about it). See slide 17 <http://www-
control.eng.cam.ac.uk/~mcs/lecture_j.pdf>

There are actually a few different analogies you can make between
electrical/mechanical devices. See the top table "Key Concept: Analogous
Quantities". This is part of the reason why I don't feel like thinking too
hard about what the inventor means when he says the analogy "breaks down" with
ungrounded capacitors.
[http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Analogs/E...](http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Analogs/ElectricalMechanicalAnalogs.html)

The inventor has created a "new analogy" where the inerter is a capacitor. I
read your post as saying the old analogies don't work. Is that correct?

~~~
colanderman
The point you're making is orthogonal to the one I was making: the force ~
voltage analogy breaks down at KCL/KVL (as well as ungrounded inductors),
while the force ~ current analogy breaks down only for ungrounded capacitors.

"Ungrounded capacitors" refers to capacitors which do not have at least one
terminal connected to the reference voltage (ground). These break the force ~
current analogy because with that analogy, capacitors, which are two-terminal
devices, are analogous to flywheels, which are one-terminal devices. The
velocity (voltage) of the second terminal is effectively zero.

Your reading of my post is close to correct. The force ~ voltage analogy is
incorrect however you look at it because KCL and KVL don't hold. The "old"
force ~ current analogy does hold except for the case of ungrounded
capacitors, which the replacement of flywheels with inerters remedies.

------
judegomila
Another interesting question. Given we can move between mechanical and
electrical systems with circuit theory. Are their other systems that we could
apply circuit theory to (i.e. non electrical and non mechanical systems).
Light and space circuits for example?

~~~
Derbasti
Audio Systems consist of electrical circuits (amplifier, player), mechanical
circuits (loudspeaker-membrane) and acoustical circuits (air, room acoustics).
All these parts can be modeled as circuits that directly interact with each
other.

You can actually calculate the electrical properties of the mechano-acoustical
loudspeaker+room or the acoustical properties of the electro-mechanical
loudspeaker+amp. This is extremely helpful when designing loudspeakers since
you can see the electrical, mechanical and acoustical properties all in one
notation.

------
judegomila
From Prof. Malcolm Smith

"I have always thought that the memristor is rather a weak concept. It is
defined as a device with a nonlinear relationship between flux and charge. A
linear memristor is the same as a resistor, so in linear circuits the element
is not meaningful. The definition does not pin down the type of nonlinearity.
So the difference between a variable resistor and a memristor is not sharply
defined. The mechanical equivalent of a variable resistor is of course a
variable damper. Variable dampers and semi-active dampers are of course used a
lot in suspension systems"

------
judegomila
From a friend: "The quantum mechanics stuff sounds very unlikely. Although if
you wanted to try and go in that direction you would have to figure out
whether circuits have a strong analogy to the Hamiltonian formulation of
quantum mechanics (i.e. no discussion of forces!) - then you would be in
business. You could then probably formulate a "quantum circuit" in which
measurements of voltage and current obey an uncertainty principle"

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iwr
What's an inerter?

~~~
eru
See <http://en.wikipedia.org/wiki/Inerter_(mechanical_networks)>.

I am not too happy with that article; does anybody have a better source?

~~~
pontifier
My own experience... I know why this concept sounds so familiar to me. I had
one when I was little.

There are many childrens toys with a flywheel and a ripcord. That system is an
"Inerter"... If the ripcord is a rigid toothed rack and pinion setup then it
can act as an "Inerter" in compression as well as tension.

------
gfodor
It's "memristor", not "memresistor"

~~~
foobar2k
actually, both are acceptable terms

------
moron4hire
Why isn't an inerter just a flywheel?

~~~
colanderman
Because flywheels have only one usable node; the other is effectively
"grounded". They're also rotational; if you're working with translational
systems (e.g. suspensions), you need something else.

An inerter, being basically a flywheel connected to a rack gear, meets both
these requirements. You have two nodes (the flywheel's axis, and the rack
gear) and the motion is translational.

~~~
colanderman
Additionally: a rotational inerter can be made by connecting the ring gear of
a differential to a flywheel. The two nodes are then the two side gears of the
differential.

