Filter Output Energy

Tim Wescott <tim@seemywebsite.com> wrote:

(snip)
> That's just a "gee whiz" thing.  But if you want to solve

> B(t) = int_0^T_s e^{At} dt, then doing it "the normal way" gets you

> B(t) = A^{-1}(e^{AT_s} - I)

> This is fine, unless A is singular.  Then you're just totally and 
> completely hosed.  But if you do the Taylor's expansion on e^{At} in the 
> original integral, you get

> B(t) = sum_n=0^\infty (At^n)/(n!)

> And that is not only mathematically possible, it's also numerically 
> tractable for quite a few realistic matrices A.

I remember supposedly learning this in math class so many years
ago, but not believing that I ever understood it.  Except we had
it exp(tA) which makes for a lot of good T.A. jokes.  

Also, if I remember it right, it also goes with characteristic
polynomials.

-- glen

glen herrmannsfeldt  <gah@ugcs.caltech.edu> wrote:

>Jerry Avins <jya@ieee.org> wrote:

>> A complete analysis accounts for the energy lost as heat and sound when 
>> the nail strikes the magnet. nevertheless, the magnet's external field 
>> is the same before the nail was picked up and after it is removed.
>
>> Do you like there conundrums? Here's another. Two identical springs are 
>> identically distorted and tied with acid-proof string into the new 
>> shape. One is set aside, the other, dissolved in acid. From the unetched 
>> spring, the energy (0.5kx^2) can be recovered. What happened to the 
>> energy stored in the spring that was etched?
>
>The stored spring energy is stored in the electromagnetic effects
>between electrons and atoms as the crystal distorts.  It is, then,
>presumably released as the atoms are released from their strained state.

That's right.  I'd quibble with "electromagnetic effects", as
it is really pure electric field effects that comprise chemical bonds 
and make them want ot have a given bond length, such that any smaller
or larger length represents strain.

Steve

On Oct 20, 7:16�pm, spop...@speedymail.org (Steve Pope) wrote:
> glen herrmannsfeldt &#4294967295;<g...@ugcs.caltech.edu> wrote:
>
> >Jerry Avins <j...@ieee.org> wrote:
> >> A complete analysis accounts for the energy lost as heat and sound when
> >> the nail strikes the magnet. nevertheless, the magnet's external field
> >> is the same before the nail was picked up and after it is removed.
>
> >> Do you like there conundrums? Here's another. Two identical springs are
> >> identically distorted and tied with acid-proof string into the new
> >> shape. One is set aside, the other, dissolved in acid. From the unetched
> >> spring, the energy (0.5kx^2) can be recovered. What happened to the
> >> energy stored in the spring that was etched?
>
> >The stored spring energy is stored in the electromagnetic effects
> >between electrons and atoms as the crystal distorts. &#4294967295;It is, then,
> >presumably released as the atoms are released from their strained state.
>
> That's right. &#4294967295;I'd quibble with "electromagnetic effects", as
> it is really pure electric field effects that comprise chemical bonds
> and make them want ot have a given bond length, such that any smaller
> or larger length represents strain.
>
> Steve

If you then attract say 20 or more nails with the magnet you find that
the field has been weakened when the nails are attached.
Remove them and the field returns to normal. hence you have used up
the energy in the field by all the nails. there is also a cooling
effect somewhere I seem to remember - magnets can be used for cooling.

Steve Pope <spope33@speedymail.org> wrote:

(snip, I wrote)
>>The stored spring energy is stored in the electromagnetic effects
>>between electrons and atoms as the crystal distorts.  It is, then,
>>presumably released as the atoms are released from their strained state.

> That's right.  I'd quibble with "electromagnetic effects", as
> it is really pure electric field effects that comprise chemical bonds 
> and make them want ot have a given bond length, such that any smaller
> or larger length represents strain.

Pretty much I always write electromagnetic instead of electric.

1: You might be in a different reference frame.

2: Electrons have spin, and a magnetic moment, even when not moving.
   (Protons and Neutrons, also.)
   
3: Electrons are in orbits, so can have an orbital component.

But yes, much of that cancels out in enough cases that electric
isn't so far off.

-- glen

HardySpicer <gyansorova@gmail.com> wrote:

(snip)
> If you then attract say 20 or more nails with the magnet you find that
> the field has been weakened when the nails are attached.
> Remove them and the field returns to normal. hence you have used up
> the energy in the field by all the nails. there is also a cooling
> effect somewhere I seem to remember - magnets can be used for cooling.

Adiabatic demagnetization.  

Put atoms with a magnetic moment in a magnetic field, cool
them off as much as possible (that is cryogenically), then
slowly (well, not too fast) reduce the field.  As the atoms
start moving again (thermal motion) they do work against the
remaining field and lose energy.

The one I remember this from is the story of the first
measurement for parity non-conservation.

-- glen

On Oct 18, 5:09&#4294967295;pm, Jerry Avins <j...@ieee.org> wrote:
> On 10/18/2011 3:35 PM, glen herrmannsfeldt wrote:
>
>
>
>
>
> > Jerry Avins<j...@ieee.org> &#4294967295;wrote:
>
> > (snip of lossless capacitor question)
>
> >> I won't give it away, but instead pose a mechanical version. Two
> >> identical flywheels, moment of inertia I, can be coupled by a dog
> >> clutch. Initially, one rotates at angular velocity w radians/second and
> >> the other is stationary. Without exerting any forces outside of the
> >> system, the flywheels are coupled by the dog clutch. Momentum being
> >> conserved, they then rotate together at w/2. Before they were coupled,
> >> the total energy was 0.5Iw^2, all in the rotating part. After the
> >> coupling, the energy of the flywheels together is 0.5(2I)(w/2)^2, or
> >> 0.25Iw^2. What happened to the rest of the energy?
>
> > I know about the capacitor, but I am not so sure about this one.
> > (Also, I don't know the dog clutch.) &#4294967295;There are many ways to
> > lose energy, and it will find one. &#4294967295;If the clutch is even a tiny
> > bit slow, there will be friction before it completely grabs.
>
> > Otherwise, there might be sound producing vibrations.
>
> > Or, due to the infinite torque the shaft could break or the
> > flywheel fly (maybe that is where the name comes from) apart.
>
> > If the shaft isn't infinitely stiff, it could absorb some
> > of the energy, either as heat (friction) or stored in the
> > bonds holding it together. &#4294967295;If there is no loss, then it will
> > be an oscillating system.
>
> Go to the head of the class. :-)
>
> A dog clutch can't slip. It consists of meshing teeth ("dogs") that can
> be disengaged by being moved axially apart and engaged by moving axially
> together. (A car's manual transmission uses dog clutches to lock
> appropriate gears to their shafts. The gears themselves remain always in
> mesh.)http://www.youtube.com/watch?v=C0aiUBf1yGo&noredirect=1http://www.youtube.com/watch?NR=1&v=vq11CusULlk
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.- Hide quoted text -
>
> - Show quoted text -

Jerry,

A common example of a simple "dog" without synchro is seen in a
motorcycle transmission. There the gears have 4 dogs protruding out of
the side of the gear so when the shifter fork moves it over and the
dogs poke into holes in the side of the adjacent gear the shaft is
forced up to speed very quickly. That is why one can shift gears very
quickly on a motorcycle. Most manual car transmissions also have
syncros effectively implemented as a cone on the side of one gear that
pushes into a conical hole on the neighboring gear and accelerates the
countershaft up to speed before the baulk ring's dog teeth engage
forcing a hard connection.

Clay

On 10/19/2011 11:06 PM, glen herrmannsfeldt wrote:
> Tim Wescott<tim@seemywebsite.com>  wrote:
>> On Wed, 19 Oct 2011 19:54:18 +0000, Steve Pope wrote:
>
>>>> If a magnet attracts a nail (mass m) from a distance h from the ground,
>>>> then it has done mgh work in doing so. When you remove the nail that
>>>> energy has to go back into the magnetic field.
>
>>> Assuming it did not become magnetized.  Then some energy has also gone
>>> into rearrangement of states within the nail.
>
>> I'm pretty sure that if the nail has become magnetized then the force
>> needed to remove the nail will be higher -- otherwise you could
>> demagnetize a magnet by repeatedly magnetizing other objects with it, and
>> I've never seen that phenomenon.
>
> There is a demagnetizing that occurs to permanent magnets when
> they don't have a closed magnetic loop.  You put a keeper across
> a horseshoe magnet when it isn't being used.  I first remember
> the story back to toy train engines, where if you take the motor
> apart, the magnet will lose much of its magnetization.
>
> There does have to be some frictional loss, or hysteresis loss,
> though, in magnetizing a hard (permanent) magnetic material.
> My though, is that the attractive force is reduced, but I believe
> also that the removal force is higher.
>
> Consider the power needed to power an electromagnet while it is
> picking up the nail, and while the nail is being removed.

Keeper shmeeper. :-)

Magnets are initially magnetized a with a keeper on because a given MMF 
produces a higher flux that way. When the keeper is removed, the flux 
drops and recovers only slightly when the keeper is replaced. (The field 
magnets of many electric motors are often magnetized in place and lose 
strength if the motor is disassembled.) Alnico and ceramic magnets don't 
need keepers when stored. They are sometimes used anyway to reduce the 
external field. The old "hard" steel magnets are protected by keepers if 
they are mechanically shocked. Just as a piece of steel can be 
magnetized by a weak field such as the earth's if jarred, it can be 
demagnetized the same way if the keeper is omitted.

Jerry
-- 
Engineering is the art of making what you want from things you can get.