(Gregory L. Hansen) wrote in message ...
In article ,
John Schoenfeld wrote:
POSTULATES OF A MODIFIED CLASSICAL PHYSICS

Inertia law:
Mass is a scalar velocity field:
Scalar form: m(v) = m0 + int(0,v) (dm/dv) . dv
Vector form: m(v) = m0 + intP(0,v) grad_v(m) . dv


1st Law of Motion:
The momentum of a body remains invariant unless otherwise acted on by a Force.
Scalar form: p = m(v) v
Vector form: p = m(v) v


2nd Law of Motion:
Force is the 1st time derivative of momentum.
Scalar form: F = (m + v dm/dv) a
Vector form: F = (m + v . grad_v(m))a


3rd Law of motion:
Interacting bodies conserve net momentum through equal and opposing Forces.


How are these modified postulates? They look like Newton's postulates to
me, except you've specialized them to a mass that varies with velocity in
an unspecified way (what's dm/dv?). It's still p=mv, F=dp/dt, and
conservation of momentum.

No, it's p = m(v)v. The different is important.

In article ,
John Schoenfeld wrote:
(Gregory L. Hansen) wrote in message
...
In article ,
John Schoenfeld wrote:
POSTULATES OF A MODIFIED CLASSICAL PHYSICS

Inertia law:
Mass is a scalar velocity field:
Scalar form: m(v) = m0 + int(0,v) (dm/dv) . dv
Vector form: m(v) = m0 + intP(0,v) grad_v(m) . dv


1st Law of Motion:
The momentum of a body remains invariant unless otherwise acted on by
a Force.
Scalar form: p = m(v) v
Vector form: p = m(v) v


2nd Law of Motion:
Force is the 1st time derivative of momentum.
Scalar form: F = (m + v dm/dv) a
Vector form: F = (m + v . grad_v(m))a


3rd Law of motion:
Interacting bodies conserve net momentum through equal and opposing Forces.


How are these modified postulates? They look like Newton's postulates to
me, except you've specialized them to a mass that varies with velocity in
an unspecified way (what's dm/dv?). It's still p=mv, F=dp/dt, and
conservation of momentum.

No, it's p = m(v)v. The different is important.

Yes, because Newton's p=mv doesn't specify that m is *not* a function of
velocity. In fact, a velocity-dependent mass had been used in the 19th
century in electrodynamics calculations, and later became known as
relativistic mass when it was realized that a quasi-Newtonian analysis of
some relativistic systems can be done by substituting
m-m/sqrt(1-v^2/c^2).

You don't have new postulates. You've specified that m=m(v), without
giving the form of m(v) or the nature or physical meaning of its velocity
dependence, and then derived a force law from the old postulates.

--
"The polhode rolls without slipping on the herpolhode lying in the
invariable plane." -- Goldstein, Classical Mechanics 2nd. ed., p207.

Uncle Al wrote in message ...
John Schoenfeld wrote:

POSTULATES OF A MODIFIED CLASSICAL PHYSICS

1) YOU ARE AN IDIOT.
2) LEARN HOW TO USE YOUR SHFIT KEY.

I am an idiot because I used caps? Think before typing, idiot (by your
own definition).

3) You are an idiot.

Think.

(Y. T.) wrote in message om...
(John Schoenfeld) wrote in message om...
POSTULATES OF A MODIFIED CLASSICAL PHYSICS

Inertia law:
Mass is a scalar velocity field:
Scalar form: m(v) = m0 + int(0,v) (dm/dv) . dv


This has me puzzled already. You appear to be saying that there is a
quantity "m" that is an integrable function of some other quantity
"v". You don't define these letters, however.

The context seems to imply that "m" refers to a mass (of what?, if I
may dare ask). I appears further that "v" refers to a velocity but as
there is only a single "m" I fail to see what velocity is meant here;
i.e. velocity of what with respect to what else?

Of course if I am interpreting the letters right, then this would only
say anything new if dm/dv was not equal to zero and since there's no
observation ever made by a human being that would lead to such a
non-zero derivative I fail to see what the purpose of this exercise
might be. You could just as well have written dm/dT to include some
temperature dependence of mass (which would also be zero). So I'm
cautiously guessing that I'm misinterpreting the physical meaning of
the variables in that equation.

Care to eludicate your thoughts to the casual reader?


m is mass v is velocity.

m(v) is velocity-dependent mass.

dm/dv is rate of change of mass w.r.t speed.

grad_v(m) is the rate of change of mass w.r.t velocity.


From the fundamental theoreom of calculus,

m(v) - m(u) = int(u,v) (dm/dv)dv

m(v) = m0 + int(0,v) (dm/dv).dv

likewise, for vector velocity

m(v) = m0 + intP(0,v) grad_v(m) . dv

"Franz Heymann" wrote in message ...
"John Schoenfeld" wrote in message
om...
"Franz Heymann" wrote in message
...
"John Schoenfeld" wrote in message
m...
POSTULATES OF A MODIFIED CLASSICAL PHYSICS

Inertia law:
Mass is a scalar velocity field:
Scalar form: m(v) = m0 + int(0,v) (dm/dv) . dv

That is brand new. Why did you change your old approach?

Wrong. It's a direct consequence from the fundamental theoreom of
calculus.
m(v) - m(u) = int(0,v) (dm/dv).dv
in vector form:
m(v) - m(u) intP(u,v) grad_v(m).dv

Vector form: m(v) = m0 + intP(0,v) grad_v(m) . dv

So which one are we supposed to choose, vector or scalar?

Newton's Laws can be expressed in Scalar form or Vector form, what's
your problem with what i have posted above?

My problem is that Newton's Laws refer only to the vector quantities
acceleration, force, momentum, etc.


1st Law of Motion:
The momentum of a body remains invariant

I think you mean constant. Invariant has to do with the behaviour
of
a quantity when changing frames of reference.

In my opinion, they are invariant and constant are equal.

No.. Before you came on the scene, the word "invariant had acquired a
quite specific usage. *Not* to be confused with "constant".
You are, of course, welcome to use exisging terms with meanings
privatew to you, but I would not advise it if you are trying to
convince folk that you are not just cheering from the side lines.


unless otherwise acted on by a Force.
Scalar form: p = m(v) v

That is not an expression for a force

That's right, it's the expression for momentum.You said it was an
expression for force. Reread what you said.


Vector form: p = m(v) v

That, also, is not an expression for a force

That's right, it's the expression for momentum.

That's not what you said.

And a force is *always* a vector.

For a lot of problems, Force can be treated as a scalar - |F|.

|F| is the magnitude of the froce vector F. Force is *always* a
vector.

2nd Law of Motion:
Force is the 1st time derivative of momentum.
Scalar form: F = (m + v dm/dv) a

There is no such thing as a scalar force.

Wrong. It's just the length of the Force vector, and v the length of
the velocity vector, which are scalars.

In that case you are still wrong, because the acceleration is a
vector.

You should learn to express yourself clearly, correctly and
unambiguously.

Vector form: F = (m + v . grad_v(m))a

These equations disagree with the definitions you gave higher up
for
force, where you called it "p" for some unknown reason.

That was a disastrous typo that I made. The "Vector" form is:

F = m(v) a + v(grad_v(m) . a)

Proof:
p = m(v) v
dp/dt = m(v) dv/dt + v(grad_v(m) . dv/dt)

Why not just keep it simple, and just say
dp/dt = m dv/dt + v dm/dt ?

Sure, since dm/dt = grad_v(m) . a.

PROOF:
dm/dt = d/dt m(v(t))
= grad_v(m) dv/dt







3rd Law of motion:
Interacting bodies conserve net momentum through equal and
opposing
Forces.

That is not a law of motion. It is deducible from the 3rd law of
motion. (I hasten to say that I refer to Newton's 3rd law, not
your
crap.)

It is Newtons 3rd law.

No. At the stage at which newton's laws are initially presented,
momentum has not yet been defined.
Newton's 3rd law says

"An action is always opposed by an equal and opposite reaction"

There is no mention of momentum conservation there. The latter is
derived a page or two later, after "momentum" has been defined".

I do most sincerely hope that you are not just aiming to give us a
repeat performance of the crap you posted earlier.

Franz

(John Schoenfeld) wrote in message om...
POSTULATES OF A MODIFIED CLASSICAL PHYSICS

Inertia law:
Mass is a scalar velocity field:
Scalar form: m(v) = m0 + int(0,v) (dm/dv) . dv
Vector form: m(v) = m0 + intP(0,v) grad_v(m) . dv

When are you going to learn the difference between definitions,
postulates and laws?

Does your law of inertia say anything about what happens to the motion
of m(v) when no force acts on it?



1st Law of Motion:
The momentum of a body remains invariant unless otherwise acted on by a Force.
Scalar form: p = m(v) v
Vector form: p = m(v) v


This can be derived directly from the 2nd law.


2nd Law of Motion:
Force is the 1st time derivative of momentum.
Scalar form: F = (m + v dm/dv) a
Vector form: F = (m + v . grad_v(m))a

This is Newton's second law F = d(mv)/dt regardles of whether m = m(v)
or not (rocket equation)


3rd Law of motion:
Interacting bodies conserve net momentum through equal and opposing Forces.

This is badly stated beyind recognition.

Conclusion: you need to take Mechanics 101.

Mike

(Gregory L. Hansen) wrote in message ...
In article ,
John Schoenfeld wrote:
(Gregory L. Hansen) wrote in message
...
In article ,
John Schoenfeld wrote:
POSTULATES OF A MODIFIED CLASSICAL PHYSICS

Inertia law:
Mass is a scalar velocity field:
Scalar form: m(v) = m0 + int(0,v) (dm/dv) . dv
Vector form: m(v) = m0 + intP(0,v) grad_v(m) . dv


1st Law of Motion:
The momentum of a body remains invariant unless otherwise acted on by
a Force.
Scalar form: p = m(v) v
Vector form: p = m(v) v


2nd Law of Motion:
Force is the 1st time derivative of momentum.
Scalar form: F = (m + v dm/dv) a
Vector form: F = (m + v . grad_v(m))a


3rd Law of motion:
Interacting bodies conserve net momentum through equal and opposing Forces.


How are these modified postulates? They look like Newton's postulates to
me, except you've specialized them to a mass that varies with velocity in
an unspecified way (what's dm/dv?). It's still p=mv, F=dp/dt, and
conservation of momentum.

No, it's p = m(v)v. The different is important.

Yes, because Newton's p=mv doesn't specify that m is *not* a function of
velocity. In fact, a velocity-dependent mass had been used in the 19th
century in electrodynamics calculations, and later became known as
relativistic mass when it was realized that a quasi-Newtonian analysis of
some relativistic systems can be done by substituting
m-m/sqrt(1-v^2/c^2).

You don't have new postulates. You've specified that m=m(v), without
giving the form of m(v) or the nature or physical meaning of its velocity
dependence, and then derived a force law from the old postulates.

Mass as a scalar function: m(v) = m0 + int(0,v)(dm/dv)dv

Mass as a vector function: m(v) = m0 + intP(0,v) grad_v(m). dv

(Gregory L. Hansen) wrote in message ...
In article ,
John Schoenfeld wrote:
(Gregory L. Hansen) wrote in message
...
In article ,
John Schoenfeld wrote:
POSTULATES OF A MODIFIED CLASSICAL PHYSICS

Inertia law:
Mass is a scalar velocity field:
Scalar form: m(v) = m0 + int(0,v) (dm/dv) . dv
Vector form: m(v) = m0 + intP(0,v) grad_v(m) . dv


1st Law of Motion:
The momentum of a body remains invariant unless otherwise acted on by
a Force.
Scalar form: p = m(v) v
Vector form: p = m(v) v


2nd Law of Motion:
Force is the 1st time derivative of momentum.
Scalar form: F = (m + v dm/dv) a
Vector form: F = (m + v . grad_v(m))a


3rd Law of motion:
Interacting bodies conserve net momentum through equal and opposing Forces.


How are these modified postulates? They look like Newton's postulates to
me, except you've specialized them to a mass that varies with velocity in
an unspecified way (what's dm/dv?). It's still p=mv, F=dp/dt, and
conservation of momentum.

No, it's p = m(v)v. The different is important.

Yes, because Newton's p=mv doesn't specify that m is *not* a function of
velocity. In fact, a velocity-dependent mass had been used in the 19th
century in electrodynamics calculations, and later became known as
relativistic mass when it was realized that a quasi-Newtonian analysis of
some relativistic systems can be done by substituting
m-m/sqrt(1-v^2/c^2).

You don't have new postulates. You've specified that m=m(v), without
giving the form of m(v) or the nature or physical meaning of its velocity
dependence, and then derived a force law from the old postulates.

typo:
Mass as a scalar field: m(v) = m0 + intP(0,v)grad_v(m).dv

In article ,
John Schoenfeld wrote:
(Gregory L. Hansen) wrote in message
...
In article ,
John Schoenfeld wrote:
(Gregory L. Hansen) wrote in message
...
In article ,
John Schoenfeld wrote:
POSTULATES OF A MODIFIED CLASSICAL PHYSICS

Inertia law:
Mass is a scalar velocity field:
Scalar form: m(v) = m0 + int(0,v) (dm/dv) . dv
Vector form: m(v) = m0 + intP(0,v) grad_v(m) . dv


1st Law of Motion:
The momentum of a body remains invariant unless otherwise acted on by
a Force.
Scalar form: p = m(v) v
Vector form: p = m(v) v


2nd Law of Motion:
Force is the 1st time derivative of momentum.
Scalar form: F = (m + v dm/dv) a
Vector form: F = (m + v . grad_v(m))a


3rd Law of motion:
Interacting bodies conserve net momentum through equal and
opposing Forces.


How are these modified postulates? They look like Newton's postulates to
me, except you've specialized them to a mass that varies with velocity in
an unspecified way (what's dm/dv?). It's still p=mv, F=dp/dt, and
conservation of momentum.

No, it's p = m(v)v. The different is important.

Yes, because Newton's p=mv doesn't specify that m is *not* a function of
velocity. In fact, a velocity-dependent mass had been used in the 19th
century in electrodynamics calculations, and later became known as
relativistic mass when it was realized that a quasi-Newtonian analysis of
some relativistic systems can be done by substituting
m-m/sqrt(1-v^2/c^2).

You don't have new postulates. You've specified that m=m(v), without
giving the form of m(v) or the nature or physical meaning of its velocity
dependence, and then derived a force law from the old postulates.

Mass as a scalar function: m(v) = m0 + int(0,v)(dm/dv)dv

Mass as a vector function: m(v) = m0 + intP(0,v) grad_v(m). dv

Okay, so you know the fundamental theorem of calculus, and you've
postulated that dm/dv is at least peice-wise differentiable. I suppose
that's progress, of a sort. At least we know the function is defined for
all v, and doesn't have pathological behavior like a Koch curve.

But that doesn't narrow it down very much unless we know dm/dv.


--
"For every problem there is a solution which is simple, clean and wrong."
-- Henry Louis Mencken

"John Schoenfeld" wrote in message
om...
(Gregory L. Hansen) wrote in message
...
In article ,
John Schoenfeld wrote:
POSTULATES OF A MODIFIED CLASSICAL PHYSICS

Inertia law:
Mass is a scalar velocity field:
Scalar form: m(v) = m0 + int(0,v) (dm/dv) . dv
Vector form: m(v) = m0 + intP(0,v) grad_v(m) . dv


1st Law of Motion:
The momentum of a body remains invariant unless otherwise acted
on by a Force.
Scalar form: p = m(v) v
Vector form: p = m(v) v


2nd Law of Motion:
Force is the 1st time derivative of momentum.
Scalar form: F = (m + v dm/dv) a
Vector form: F = (m + v . grad_v(m))a


3rd Law of motion:
Interacting bodies conserve net momentum through equal and
opposing Forces.


How are these modified postulates? They look like Newton's
postulates to
me, except you've specialized them to a mass that varies with
velocity in
an unspecified way (what's dm/dv?). It's still p=mv, F=dp/dt, and
conservation of momentum.

No, it's p = m(v)v. The different is important.

Then please explain this important difference between
p = mv
and
p = m(v)v

Franz