But I think you will agree that a PM rotating relative to some permeable material will create mechanical energy gain (during the attractive approach) only for that energy to be lost (during the attractive recede).

Yes

I disagree. First any two currents that are "fighting" each other and are both sinusoidal, the resulting current as also sinusoidal.

While you are correct that a sum (or difference) of two sinusoids yields a sinusoid (or zero) regardless of their phase, the induced current is not sinusoidal because the magnetic flux cutting the crossection of the winding does not change sinusoidally in the rotor/pole geometry that you have drawn. So sinusoidal LC current + non-sinusoidal induced current = non-sinusoidal total current.

This is a minor point in our discussion that has no bearing on your operating principle.

Second the moving magnet does not induce current, it induces voltage.

Voltage is just a potential, in other words "what might be". An inductor is a current device and a real event in it is the current flow. An inductor with voltage across it but without current flowing through it (e.g. an open inductor) is equivalent to nothing. It does nothing, it might as well not be there at all.

So forgive me if I analyze inductors in terms of currents and capacitors in terms of voltages.

(The way Lenz's Law is expressed leads to wrong statements like your "induces current in the winding that is in opposite direction to the current discharging from the capacitor".)

I also have a problem with the Lenz law, however it is not about the precedence of voltage over current but my objection is that it is a qualitative law and not a quantitative law.

I'd like to have a quantitative Lenz law stating, that the current induced in an ideal shorted inductor generates its own magnetic flux that acts to maintain the total flux penetrating the inductor, at a constant level. Any imperfections of the inductor, such as resistance and self-capacitance are a different story.

To establish the direction of current you have to look at the effect that the induced voltage has on the circuit, and the effect of that induced voltage is not as you state.

Both the direction and magnitude of the induced current are as I state. This can be seen merely with a CSR and an oscilloscope.

An inductor is a current device and it is the current that generates magnetic flux in it - not voltage.

You do not have two currents fighting each other.

You do have fighting currents in your device, because the induced current is subtracted from the current delivered by the capacitor.

You have a capacitor discharging current into an impedance where the voltage is changing sinusoidally, and that leads to that current also being sinusoidal. It is exactly like the capacitor being discharged into an inductor.

Yes, that is the shape of the current flowing in the inductor when it is supplied by voltage from a capacitor. A classic LC behavior. But the induced current is a different story - it is neither sinusoidal (because the flux is not) nor in the same direction as the current delivered from the capacitor.

Totally disagree. Again you are fixated on induced **current** whereas changing flux induces **voltage**.

It is not an accident nor fixation. The cherished concept of induced voltage (Faraday's law) is useless when analyzing the response of an ideal shorted inductor to a changing external flux.

And the proper approach to analysis is to start with ideal components first and add the imperfections later.

Any current that flows as a result of that voltage has to take account of the load into which that current flows.

Yes, but the concept of current caused by voltage (Ohm's law i=V/R) is not always useful and blindly following it can lead you down the garden path. Analysis of currents induced in inductors, subjected to changing external flux, is a perfect example of this.

Just consider whether the calculation of induced voltage in an ideal shorted inductor, subjected to a changing external flux, leads to any good answers ...if you try, you get i=V/0 from the Ohm's law and no clue to what the induced current in that inductor really is. (...and it is neither infinite nor zero).

I remind you, that only current flowing in the inductor represents the energy stored in the inductor at that moment and only the current produces any measurable effects.

A short across the coil cannot possibly be considered the same as a pre-charged capacitor. The current cannot possibly be the same for those two cases.

Of course it is not, because capacitor is a voltage device and a coil is a current device. A shorted coil stores energy in the form of current and an open capacitor stores energy in the form of voltage....or internally as magnetic field and electric field, respectively. The behavior of the LC circuit stems from sloshing of the energy between these two forms.

That should really be stated as "a powered winding attracts the rotor (if the powering voltage is greater than the induced voltage so as to drive current of the correct polarity).

Involving voltage in inductor analysis is unnecessary and leads down a garden path.

I would make the same objection if you were fixated on current in capacitors.

Now I have to write that you are "fixated" on voltage instead what really matters in an inductor - current. Voltage across an ideal shorted inductor cannot even be measured and a shorted inductor is the active inductor.

An open inductor is inactive and it neither stores energy nor builds the magnetic flux, while a shorted inductor - does.

Conversely, a shorted capacitor is inactive and neither stores energy nor builds the electric field, while an open capacitor - does.

If the powering voltage is smaller than the induced voltage the current flows in a direction to create repulsion, of which the shorted coil is the limiting case of zero applied voltage.

I agree but the same conclusion can be reached just analyzing currents in the inductors.

The capacitor powering an inductor is a variable voltage source and as you probably know, the internal impedance of an ideal voltage source is zero, so the inductor is effectively shorted by zero impedance and and its response to an external changing flux is the same as that of a shorted inductor.