Well laddies. Both Bertrand Russell and Rene Descartes were both Philosophers and excellent Mathematicians. The problems that I have with Philosophy and Psychology as well is that the professors want you to regurgitate others' thoughts, and put no value on any other original ideas of the student. It's easy to feel insulted when your ideas are dismissed out-of-hand. I chalk that up to soft-headed soft scientists to appease myself.

Time for a little Operations Research (Scientific Management) instruction :

As for quadratic equations they are useful for many practical ideas in life. Remarkably they will find the optimum selling price for maximum profit if the demand and cost curves are known (these can be measured rather easily). All of this without using Calculus! It is very useful in business to be able to see this clearly.
All quadratics are parabolas, and the optimums (optima for you latin scholars) in this case are at the vertices of parabolas.

They also describe the flight of an artillery or mortar shell which allowed myself and others to identify the location of the weapon. We did have to figure in the Coriolis effect, air drag, temperature and humidity as well but we were basically dealing with a parabola.

I Think your rocket example should be like this F = (dm/dt)*(dv/dt )

No;. Tullio's equation is exactly what Einstein started with to get to E=MC ^2.

As in Tullio's equation, Einstein asked what would happen if mass were not a constant. Apply this equation to the momentum change when two moving objects collide and rebound and you will get to Einstein's equation. The miracle and eureka moment was that it was actually true that mass and energy were related.

I Think your rocket example should be like this F = (dm/dt)*(dv/dt )

No;. Tullio's equation is exactly what Einstein started with to get to E=MC ^2.

As in Tullio's equation, Einstein asked what would happen if mass were not a constant. Apply this equation to the momentum change when two moving objects collide and rebound and you will get to Einstein's equation. The miracle and eureka moment was that it was actually true that mass and energy were related.

According to Newton in his second law of motion.
constant mass. F = m*(dv/dt)= m*a.
variable mass. F = (dm/dt)*(dv/dt) = (dm/dt)*a.

The first derivate is the tangent for a point in a function.
The second derivate gives you when it's equal to zero a maximum if positive and a minimum if negative.

An Integral is the area below the function.
In this case it's the momentum P = m*v*v/2.

The first derivation by Einstein
https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence#The_first_derivation_by_Einstein_.281905.29
Eureka

I simply apply the rules of derivation to a product of two variables. My equation is exact, ask any mathematician.
Tullio

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I simply apply the rules of derivation to a product of two variables. My equation is exact, ask any mathematician.
Tullio

Mine is also exact. And generel:)
Works in every cases.
Here is my Products: mass as a function of time (dm/dt) and speed as function of time (dv/dt).
Multiply them and you get the force.
Another notation you can use is the dot notation over m and v that I cannot write.
F=dot m * dot v

I have a uni degree in math, thermodynamics, classical mechanics and quantum mechanics.
I have to know these thing in my work. Not QM:)

I have followed four math courses, Analysis 1,Analysis 2,Analytical Geometry, Analisi Superiore. My Thesis was based on Lie Group theory and employed non compact Lie Algebras such as SU(N,1). It was published on IL Nuovo Cimento in September 1967.
Tullio

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I have followed four math courses, Analysis 1,Analysis 2,Analytical Geometry, Analisi Superiore. My Thesis was based on Lie Group theory and employed non compact Lie Algebras such as SU(N,1). It was published on IL Nuovo Cimento in September 1967.
Tullio

1967:)
Well At that time I didn't know that math was a science.
I have had some very bad teachers in highschool.
One couldn't explain what a function is!
That year I got the lowest grade you can get:(

Analisi Superiore? What is that?
An analys that are superior to other analysis?

Let's call it a Linear Vector Algebra It is the theory of Linear vector spaces, such as Banach spaces, which have a norm (a kind of distance) and are complete, that is a Cauchy succession always includes a point in that space. A Banach space becomes a Hilbert space if it has a scalar product, besides a vector product. All equations of Quantum Theory use Hlibert spaces (See "Quamtum Mechanics" by P.A.M.Dirac or "La mecanique quantique" by Albert Messiah). Hilbert vectors can be projected in energy-momentum spaces and become the Schroedinger eigenfunctions, more easily understandable since they are wavefunctions. Chemists call them "orbitals" since they define the possibile "orbits" of electrons in atoms and molecules. A molecular orbital is often defined as a Linear combination of atomic orbitals, and is calculated by computers using various approximate methods, such as Hartree-Fok and density functional theory.
Tullio

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To clear this up on a more basic level:


Speed times mass is not force. It is MOMENTUM p=mv

FORCE is the change in momentum F=d/dt (mv)

Taking the total differential of the momentum equation and allowing mass to be a variable will give the equation that Tullio put forth.

F = mdv/dt + vdm/dt.

The first derivation by Einstein

That does not explain the derivation that I was alluding to. I recommend the treatment in "Theoretical Physics" by Blass.

To clear this up on a more basic level:


Speed times mass is not force. It is MOMENTUM p=mv

FORCE is the change in momentum F=d/dt (mv)

Taking the total differential of the momentum equation and allowing mass to be a variable will give the equation that Tullio put forth.

F = mdv/dt + vdm/dt.

Momentum is not a force
Explain this to me. "F=d/dt (mv)" What is d?
Is d/dt=mv? That's not math notation.
http://setiathome.berkeley.edu/forum_thread.php?id=77790&postid=1705559#1705559

"Speed times mass is not force."
Of course not. I haven't said that.

"MOMENTUM p=mv"
Wrong. MOMENTUM is P=m*v*v/2



It was Isaac Newton that refined the math that Descarte come up with in the 17th centuary. Works even today...

d/dt is a differential operator which operates on a function, in our case the product mv.
Tullio

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d/dt is a differential operator which operates on a function, in our case the product mv.
Tullio

d/dt means nothing to mathematicians.
It's not a differential operator. "*" is an operator.
dv/dt and dm/dt are factors in an equation.
Factors are a mathematical term for a component in a multiplication.

d/dt means nothing to mathematicians.
It's not a differential operator. "*" is an operator.
dv/dt and dm/dt are factors in an equation.
Factors are a mathematical term for a component in a multiplication.

dv/dt and dm/dt are not divisions. In a different notation you could use a dot above v and above m to signify they are derived with respect to time.Operators are commonly used in quantum physics. They form Lie algebras.
Tullio
Mathematical foundations of quantum mechanics, by George W. Mackey, W.A.Benjamin, 1963, pag. 10
d/dt f(a+tv) = lim f(a+tv) -f(a)/t t->0
Note the d/dt operator

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d/dt means nothing to mathematicians.
It's not a differential operator. "*" is an operator.
dv/dt and dm/dt are factors in an equation.
Factors are a mathematical term for a component in a multiplication.

dv/dt and dm/dt are not divisions. In a different notation you could use a dot above v and above m to signify they are derived with respect to time.Operators are commonly used in quantum physics. They form Lie algebras.
Tullio
Mathematical foundations of quantum mechanics, by George W. Mackey, W.A.Benjamin, 1963, pag. 10
d/dt f(a+tv) = lim f(a+tv) -f(a)/t lim t=0
Note the d/dt operator

Math is case sensitive.
D/Dt is not an operator. It's a volume.
DF/Dt = dF/dt + u (vector Arrow velocity) * rot of the (vector arrow) * F.
It's used in fluid mechanics and QM.
https://www.youtube.com/watch?v=bPMN9VDn7NA

I shall not write any longer. Never spoke of D/Dt. DD for me is an operator to download files in UNIX..
Tullio

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I have a uni degree in math, thermodynamics, classical mechanics and quantum mechanics.

I have to say that I am very surprised ......

...why?

I have a uni degree in math, thermodynamics, classical mechanics and quantum mechanics.

I have to say that I am very surprised ......

Why? There are more people here in this forum that have that knowledge!

Wasn't this thread handling Philosophy? :D

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rOZZ
Music
Pictures

Isaac Newton, "Philosophiae Naturalis Principia Mathematica"
Tullio

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