5 ms·

Interesting, I'm curious why this analogy was chosen, and not the other way around. Current as torque and voltage as (rotational) velocity would seem to allow

Interesting, I'm curious why this analogy was chosen, and not the other way around. Current as torque and voltage as (rotational) velocity would seem to allow the junctions to be much simpler -- just a gang of gears on a single axle, rather than the differential mechanism used here -- since torques (like current) add at an axle/junction, while rotational velocity (like voltage) transmits through an axle/junction. Edit: I suppose a/the major reason is to get the resistance = friction analogy down. With current as torque, friction acts as conductance. E.g., a constant-torque/"current" motor would need to be held still (high friction) to prevent its speed/"voltage" from growing, whereas with the equivalent electrical circuit, you need to short the terminals (low resistance) of a current source to do the same. I suppose the reason for this seeming discrepancy is that, in an electric circuit, wires are separated by high resistance. But in a physical circuit, "wires" are separated by low friction (= not touching). Flipping around the natural behavior of a junction allows you to take the dual of the entire circuit, thus causing the behavior of resistance and friction to line up.

mdiesel 5y ago
All natural systems are spring+damper. That means they're effected in the same way by a difference in potential (spring) and also resistance to rate (damper). This isn't so much analogies, more that the physics of natural systems means they're governed by 2nd order differential equations, so really do behave the same. More importantly, they're all forms of energy and transferable. Power=IV=Fv=TO=PQ.
- gugagore 5y ago
  I don't think I understand the point you are making. Power = product of two quantities. You have these two quantities in various domains: I and V, F and v, T and O, P and Q, ... The analogizing comes from saying "I is like P and V is like Q", or vice versa. 2nd order ODEs are very common, and I agree that it is unifying to see different systems modeled by the same equation. But I think more fundamental than that is the understanding of "through" and "across" variables, the notion of a "port" [1], and series/parallel toplogies for combining two one-port components to form a new one-port component. You could still make an analogy between domains, even if you don't have second-order ODEs. This is clear even from your comment because, note that a spring+damper is going to be a first-order ODE. You would need moving mass to store kinetic energy, in addition to the spring to store potential energy. [1] https://en.wikipedia.org/wiki/Port_(circuit_theory) https://en.wikipedia.org/wiki/Port_(circuit_theory)

mdiesel 5y ago

All natural systems are spring+damper. That means they're effected in the same way by a difference in potential (spring) and also resistance to rate (damper). This isn't so much analogies, more that the physics of natural systems means they're governed by 2nd order differential equations, so really do behave the same. More importantly, they're all forms of energy and transferable. Power=IV=Fv=TO=PQ.

gugagore 5y ago
I don't think I understand the point you are making. Power = product of two quantities. You have these two quantities in various domains: I and V, F and v, T and O, P and Q, ... The analogizing comes from saying "I is like P and V is like Q", or vice versa. 2nd order ODEs are very common, and I agree that it is unifying to see different systems modeled by the same equation. But I think more fundamental than that is the understanding of "through" and "across" variables, the notion of a "port" [1], and series/parallel toplogies for combining two one-port components to form a new one-port component. You could still make an analogy between domains, even if you don't have second-order ODEs. This is clear even from your comment because, note that a spring+damper is going to be a first-order ODE. You would need moving mass to store kinetic energy, in addition to the spring to store potential energy. [1] https://en.wikipedia.org/wiki/Port_(circuit_theory) https://en.wikipedia.org/wiki/Port_(circuit_theory)