Permanent magnet motor article

Do non-conservative potential perpetual running machines exist ?
by W.D.Bauer © released 26.6.97 some additions 8.7.97 revised 3.5.98
It is shown that a system of coupled cog-wheels obeys a non-conservation relation of angular momentum.
 It is shown shown by an example that a changing charge in a (conservative) ratched potential is subjected to a non-conservative force field which generates a perpetuum mobile cycle. It is shown that this model supports the perpetuum mobile claims of the Watson-Hartmann SMOT device only if it is assumed that magnetisation of the moving iron material depends from field gradient dH/dx as well. A nonlinear dependence of magnetisation from the field H alone gives no perpetuum mobile cycle. This fact is analogous to the known behaviour of electric cycles of non-linear capacity and coil.


1) Introduction
Because the positive messages grow in number that there exist already some working perpetuum mobile the question arises how this can be reconciliated with usual physical laws. The usual killer argument of physics against this claims is normally that all known fields can be described by potentials fields which conserve energy during one cycle in the field. Indeed, this argument gives a good hint where not to look for a perpetuum mobile, or which proposals will not work. But if we have a more precise look for not mentioned additional implicit assumptions laid down for energy conserving potentials we see quite easily that some these machines could run indeed.
Known to the author are the following implicit assumptions which must hold for conservation of energy and angular momentum additionally:

 for angular momentum conservation:
If we have a composed system consisting of some (general) charges in a field (i.e. mass particles in gravitational fields, magnetic poles in magnetic field, electric charges in electric fields) the charges have to be either independent from the neighbour charge or the they have to be coupled to the neighbours by central forces [1].

 for energy conservation:
1) the generating potential must be independent from additional variables as parameters, i.e. especially from time .
2) Charges in conservative field which generate the conservative force field by coupling to the field have to be constant or conserved.
We will see that if this assumptions must be dropped -because of the mechanic design of the construction- conservation laws break down and perpetuum mobiles become possible principally.

2) Angular moment non-conservation
It is well known fact that conservative force field do not allow any energy gain on any closed path in a potential field. For free moving systems angular momentum is conserved as well.However, this feature can be destroyed if we mount general charges in a general potential field on coupled cog wheeels or on similar working lever mechanisms. This is illustrated in fig.1 for two charges mounted on a cog wheel each. The radiuses of the wheel have the ratio n = r 1 /r 2 . For uncoupled charges (no cog wheel coupling) the torques on the one-dimensional periodic circular path of the charges can be expressed by

where  are the angle position of the charge on the disk  are the angular momentum, is the torque and V is the potential of the(general) force field. For coupled wheels the equations for the torques are

It is interesting to multiply equation 2b) by n and to add it to equation 2a). We get

This equation represents the "conservation of angular momentum" for this system. It is clear that this equations deviates from usual conservation of angular momentum.
However, the energy of this system is conserved. This is case because both equations fulfill the condition  as well. Therefore the system of equations can be written dependent only from one variable instead of two. Therefore, because the system is only one-dimensional, the potentials of both charges on the wheels can be obtained by integration, the system is conservative regarding energy and allows no energy gaining perpetuum mobile cycles.

3) Energy non-conservation
 On an official level of science there exist publications about so called rachet potentials (periodic potential with an assymetric shape) dependent from time which allow to gain work from noise [1.] However, the practical application of these ideas is still at an rudimentary level.
On the other side, the newest claim of a successful perpetuum mobile permanent magnetic design is by Greg Watson [3] who got running on a circuit the linear patent proposal of Hartman[4]. In the meantime this design has been successfully reproduced and works[5].
In this section we will present a simple one-dimensional mathematical model with a space dependent ratched potential which explains the working of Watson's SMOT,RMOD and variations therefrom quite naturally.
To get such a machine working we need
1) an assymetric shaped periodic, cyclic or linear, general potential field  (called ratched potential) which allows to derive a general conservative vector field E(x)= -d/dx therefrom.
2) a non-constant general charge q(x) dependent from path x coupling to the field E(x)
These ingredients allow us to build a cycle which work integral can be positive or negative depending on direction, which is indicative for perpetuum mobile action.
We illustrate this here by a very simple mathematical model example. We assume a charge which is dependent from x and obeys the relation

We assume a periodic ratched potential V(x) obeying the relation

Therefrom, the field E(x) can be derived according to the definition E(x)= -d /dx of the vector field of a potential

The force F(x) of the field E on the charge q is F=q.E . Therefrom, the work of one cycle can be calculated to

We see here that W is negativ indicating a energy gain during a cycle. Fig.2 shows the potential  and the energy W gained versus x. Note that if the charge is chosen constant then W=0. The same would be probably the case if we choose a space dependent charge q(x) and any symmetric periodic potential V during the cycle, because then both function multiplied under the integral become symmetric and cancel to zero.
To be more practical and concrete we have to identify the mathematics with the physics. First, we test out a case of a isotropic nonlinear magnetic material with a unique  which call the simple SMOT and which will not work -as we will see below:
If we move a magnetic permeable body in a magnetic field and neglect thermic losses the formula describing the energy conversion of mechanic energy into magnetic energy and vice versa is



where M is the polarisation per volume element  and H is the magnetic H field and B is the magnetic B-field. The second equation holds because the added cycle integral including the vacuum polarisation term H is zero.
Now, because  is symmetric resp. to H=0,  can be written in a Taylor expansion expanded around H=0 with the second order term as lowest order term.

with  and 0=const. being the initial permeability at H=0. Using the definition :=1/2.H2 we rewrite (8) using (9)

If the function in the circle integral is unique and does not depend from other parameters the circle integral coincides with a usual integral. Because of the periodicity of the function H(t,x') is the same before and after a cycle of the time, it follows and therefore

The whole consideration can be extended to a ferrite with  changing with x' if eq.(9) holds locally. Therefore, in this respect the simple SMOT behaves formally completely analogous to other null-result problems arising in the electronic perpetuum mobile scene, i.e. the charge and discharge of an nonlinear time invariant coil or capacitance. This can be shown as follows:
According the theorem of Tellegen in a network of 2-pole element the energy conservation equation of power of the single elements holds
The electronic elements may be taken quite arbitrary. These elements may be resistors, capacitors inductors and they even may include parts of more pole electronic components as a primary or secondary of a transformer for example.
In order to discuss the overunity capability of electronic components it is more convenient to write down the balance equation above in terms of energy and to restrict the discussion on cyclic electronic processes. Therefore we get the energy balance equation for a cyclic process of length 
Now we can distiguish the electronic components as energy source if  U dQ < 0 and as electric consumer if  U dQ > 0. To illustrate things these cases can be represented as working areas of different orientation of the cycle.
Now, for people believing in overunity the questions arises whether passive electronic components can be brougth into a energy sucking state with negative electric work area when they act as electric energy sources contrary to the usual positive dissipating work area of a resistor for example. We will see that for any conventional non-linear time invariant components the result is zero. The energy of the electric cycle of a nonlinear capacitor is
An analog consideration can be done with an nonlinear inductivity because in this case holds
where  inductivity.
In both cases (eq.14 and 15) the result is zero for a periodic cycle of time  because U()=U(0) and I()=I(0).
It is clear that both cases are formally completely analogous to the SMOT as well, see Tab.1.
Therefore, some TEP-circuits proposed by us probably does not work as well and the effects are due to energy input through the parasitic capacitance of the FET. It should be noted that some of this facts are well known and can be found in textbooks of network theory[2].

Tab.1: analogy between SMOT and electric cycles with nonlinear inductivity and capacitance
for these system no perpetuum mobile action is possible

system  parametrisation  energy 1  energy 2
simple SMOT  path x  magnetic field  mechanical energy
inductivity  time t  magnetic field  electric current
capacitance  time t  electric field  electric current

Our result is contrary to the suggestion given in our last version of this SMOT article. There we overlooked the fact that in our model substance  is dependent from H and not from the field  which makes the big difference.
Therefore, the question arise whether cyclic non-conservative processes work can exist at all. We will show that the existence of cycles with overunity efficiency depends from the question whether a material can be found whose material constant  depends on a field like  as well.
 In the most general case it holds the matrix equation  as constitutive equation for any ferromagnetic material due to the field character of the electromagnetic theory. Therefore to run a SMOT  we need

1) material with  dependent from 
2) an assymmetric ratched field H(x) from outside

If an additional contribution due to this inhomogenity exists the formula for  can be expanded at H=0 and we get

With the definition :=H2/2 , and using eq.(8) we get finally



This is a expression which is nonzero for nonsymmetric periodic functions of (x) in a cycle.
Due to the theory of ferromagnetism by Landau [8] terms of  are possible for the free energy potential. These terms are attributed to anisotropy of magnetisation caused by Bloch walls of the magnetic domains in the bulk. At the moment the author does not see clearly whether it is correct to apply this theory to the present problem and whether material can be designed appropriately by making the material grains of the bulk so very fine that the inhomogenity terms get quantitatively relevant. It should be noted that Bruce Vandeayrs [5] SMOT contained metallic powder as ferromagnetic material and another overunity claimed motor of Bill Mullers motor [9] does it as well.

4) Conclusion
If we regard mathematics every differential equation has its own conservation laws[10]. It is clear that real systems and consequenly its equations describing the physics can be chosen the conservation law coinciding with the usual conservation laws of physics. But I think I have shown that the possibility of other choices exist as well, especially if the symmetries of fields are broken.

1) T.W.B. Kibble  Classical Mechanics (second edition) p.127  Mc Graw Hill London 1973

2) Prof Hänggi's (Universität Augsburg) literature list

3) Greg Watson's homepage

4) E. Hartman U.S. Patent Nr.4215330 date 29.7.1980
look at the IBM patent server

5) 20.6.97 at mailing list freenrg-l at
see as well at J.L. Naudin's server

6) Gary's magnetic motor
Harper's new monthly magazine March 1879, p.601-605

7) R. Unbehauen Grundlagen der Elektrotechnik 2 4.Aufl. Springer, Berlin 1994

8) L.D Landau, E.M. Lifshitz Elektrodynamik der Kontinua Vol.8
Lehrbuch der theoretischen Physik Akademie Verlag Berlin 1985

9) Gottfried Hilscher Energie für das 3.Jahrtausend VAP-Verlag Wiesbaden 1996

10) S.C. Anco, G. Bluman Phys. Rev. Lett. 78 (1997) p.2869-2873
Direct construction of conservation laws from field equations


Fig.1: How to generate a system not-conserving angular momentum

Fig.2: Potential V versus x and work W versus x of a ratched potential ona non constant charge. Is is shown that the potential is strictly periodic -contrary to the work which rises from cycle to cycle, comp. text

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