Newton's laws in variable mass systems

[Dickfore]

You have been given a reference to exactly such a derivation twice in this thread. Here they are (both link to the same article):

What equation exactly in the first reference has the derivation?

 

[D H]

Equation (2). Technical papers don't need to spell out the blatantly obvious; they just need to say that some result is blatantly obvious (e.g., the stock phrase "the reader can readily see"). From the paper (emphasis mine):

If we consider the simple case of a variable mass, and we write Newton's second law as:

$$\vec F = m\frac{d\vec v}{dt} + \vec v\frac{dm}{dt}$$

we can easily see that it violates the relativity principle under Galilean transformations.​

Be honest: Do technical papers need to spell out the obvious?

 

[Dickfore]

Exactly! And, if you understood this as an argument in favor to your claim, you are illiterate when it comes to scientific literature.

 

[D H]

No. I placed this paper in camp 3, Newton's laws don't apply to variable mass systems, which in my mind is a stick one's head in the sand position. Aerospace engineering is plain old Newtonian mechanics. We've been flying for over a century now, and flying modern rockets for nearly that long. Descriptions of flying machinery is almost always done in a Newtonian (read: not Lagrangian) sense. So to say that Newtonian mechanics doesn't apply to such devices is just silly.

 

[Dickfore]

No. I placed this paper in camp 3, Newton's laws don't apply to variable mass systems, which in my mind is a stick one's head in the sand position. Aerospace engineering is plain old Newtonian mechanics. We've been flying for over a century now, and flying modern rockets for nearly that long. Descriptions of flying machinery is almost always done in a Newtonian (read: not Lagrangian) sense. So to say that Newtonian mechanics doesn't apply to such devices is just silly.

Your position has clearly failed. Do not change the thesis. It would be the most mature thing you can do if you admitted your error about the fallacious Transformation Law that you presented in post #14.

 

[D H]

Please. I have not changed my thesis and there is no flaw in post #14 given the definition F=dp/dt.

 

[D H]

There is some flawed mathematics in this thread. Post #61 implicitly assumes there is no momentum flux inside the control volume -- i.e., it assumes that all particles are moving at the same velocity.

 

[Dickfore]

lol, keep striking.

 

[D H]

The only swingin' and missin' is yours. This is a standard problem in graduate level aerospace engineering classes. A rocket is not a point mass. The center of mass of the fuel is not the center of mass of the vehicle as a whole. As fuel is consumed the overall vehicle's center of mass will move inside the vehicle. This motion of the center of mass has an effect on vehicle dynamics. Challenge to you: What are the equations of motion for such a rocket?

 

[Dickfore]

Everything in that post is well defined. You didn't read it.