3 ms·

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 electr

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.

moron4hire 16y ago
No, charge would be equivalent to potential energy, resistance would be equivalent to friction, etc. You're confusing a property and objects that effect that property.
colanderman 16y ago
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 16y ago
  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 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/ElectricalMechanicalAnalogs.html 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?
  - colanderman 16y ago
    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.

moron4hire 16y ago

No, charge would be equivalent to potential energy, resistance would be equivalent to friction, etc. You're confusing a property and objects that effect that property.

colanderman 16y ago

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 16y ago
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 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/ElectricalMechanicalAnalogs.html 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?
- colanderman 16y ago
  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.