Is there a 4th missing component in the mechanical world?
judegomila.com
judegomila.com
(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.
You can build the memresistors out of combinations of components but it doesn't allow for miniaturization and low power usage. I.e. the application in RAM is going to be huge!
In the end, like I said above, you show me memristors that blow transistors out of the water and I'll start designing with them tomorrow.
(Of course, I have my reservations that they'll be much help for analog circuit design: with regard to CMOS, the last few generations have been friendly to digital designers but decidedly unfriendly for analog design. (Give me 0.18u or 0.13u CMOS any day.)
Really, almost all analog CMOS chips, even at advanced nodes, still have older, bigger devices integrated as well. Even at 65nm, good old 0.35u or 0.25u devices are used for i/o and a large amount of analog design because the advantage of using smaller devices is between somewhere between negligible and negative for a lot of designs.)
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.
http://www.quora.com/What-is-the-mechanical-element-equivale...
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.
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.
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...
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?
"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.
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.
You can also model some hydraulic systems using components analogous to electronics (flow=current, pressure=voltage, pipes=resistance). For example a certain pressure applied to a pipe of given size (cross-section + length) and material will result in a predictable rate of flow.
In other words, anything you can describe as a differential equation has an analogous circuit. In fact, I've read the claim (though I cannot, for the moment, find the reference) that the term analog was first applied to circuits which were being built to solve LTI differential equations: the circuit was the analogue of the equation, thus it was an analogue (eventually, just analog) circuit.
"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"
I am not too happy with that article; does anybody have a better source?
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.
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.