Are fictitious forces necessary to solve certain problems?

[cmb]

I haven't a single contention with you in regards constructing the procedures for handling non-inertial frames. But if we're building on what has gone on since Newton, better to say 'according to the d'Alembert Principle' rather than 'by Newton's 2nd law', no?

The OP's question, "are fictitious forces necessary for some problems", is quite clearly NO. But like any mathematical transformation, they may well make a problem a whole lot easier.

...And before we go back to the 'how could weather predictions do without using Coriolis forces', I'd cheekily point out that they hardly seem to qualify as 'accurate' with it!

 

[D H]

My point that it is not right to both cite Newton and also claim 'non-inertial accelerations' in rotational frames.

Your point assumes that physics hasn't changed since Newton's time. It has. Your point is invalid.

What we call Newtonian physics today is radically different from that set forth in Newton's Principia. Newton's reasoning was highly geometric; the Newtonian mechanics of today is highly algebraic. Newton's calculus is quite different from the calculus as taught and used today. Newton didn't have vectors; we do. Newton didn't have a solid concept of what constitutes a frame of reference and thus couldn't generalize that concept to non-inertial frames; we do.

There must be a force on the helicopter to maintain its relative position with respect to another accelerating body. I don't see how we are disagreeing, this is just terminologies.

This is much more than a disagreement over terminologies. You are unwilling to accept the validity of non-inertial frames. Conceptually, all frames of reference are equally valid.

However, just because all frames are equally valid conceptually does not mean that all frames are equally valid in practice. Given some problem to be solved, some frames will be much easier to work in than others, and some frames will yield much better accuracy than will others. Which frame is easiest to work in and which will yield the greatest accuracy depends very much on the problem at hand.

 

[cmb]

Your point assumes that physics hasn't changed since Newton's time. It has. Your point is invalid.

What we call Newtonian physics today is radically different from that set forth in Newton's Principia.

This seems to have become an argument picking me up on the way I am saying stuff, not on the conclusions to be reached wrt OP's question.

I mean, imagine it if you were actually right; DH; "Your point assumes that physics hasn't changed since Newton's time. It has."! Now you'll argue that 'physics' is the 'human construction', not really the actual way things work in the universe. And so we debate words, and words, and words on words, but not the actual physics, so I will exit, promtly, at this point...

 

[D H]

I mean, imagine it if you were actually right; DH; "Your point assumes that physics hasn't changed since Newton's time. It has."! Now you'll argue that 'physics' is the 'human construction', not really the actual way things work in the universe.

That is exactly right. Physics, and all the sciences, are a human construction. The goal of science is to perfectly describe "the actual way things work in the universe." Our current knowledge is not perfect. There is, and will probably always remain, room for improvement. The goal of perfectly describing reality is to some extant an unattainable goal, but we can can get ever closer. This improvement of our knowledge and understanding is one of the driving factors that justify scientific research.

 

[JeffKoch]

The second word in the subject line answers it's own question: There is no such thing as a fictitious force, so obviously the answer is "no".

If you refer to forces that are best described, and are felt and can do work, in non-inertial frames of reference, I don't know if the answer is a definitive "yes" or "no", but it makes sense to use descriptions of forces appropriate to a frame of reference when you are trying to understand what is happening in that frame of reference.

 

[D H]

The second word in the subject line answers it's own question: There is no such thing as a fictitious force, so obviously the answer is "no".

Better said: There are no fictitious forces in an inertial frame.

When the question implicitly or explicitly asks for the forces in a non-inertial frame (e.g., post #3), the answer is "yes". There is no way to answer the question Hootenanny asked in [post=3549926]post #3[/post] without using fictitious forces.

When the question is restricted to predicting outcomes as MikeyW proposed in [post=3549947]post #6[/post], the answer is, in theory, "no" since there are no fictitious forces in an inertial frame. In practice, the answer is still "yes". I gave several examples in [post=3549961]post #8[/post] where nobody in their right mind would even begin trying to answer the question from the perspective of an inertial frame.

 

[harrylin]

[..]
Then my term 'perceived acceleration' is simply your 'co-ordinate acceleration'.
[..]
Problem is, it is the wrong use of Newton's 2nd law. You cannot claim to use the 2nd law (acceleration is proportional to force) if the whole framework of co-ordinates is, itself, rotating. I can hear my maths master saying it now; 'WRONG! You HAVE TO write the equation of motion.'

Newton's 2nd law specifically refers to the notion of a linear function "Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur". (I don't think we need to speak latin to figure out the meaning of this!)

Right - it's an improper use of Newton's laws, misapplying them with respect to rotating frames.

However, the point of this thread is to put the claim to the test that this improper utilisation is very useful, or even necessary to solve certain problems. And regretfully, so far not a single calculation example with fictitious forces of such a case has been given... Thus the challenge remains open to those who made such claims.

 

[harrylin]

[..] I gave several examples in [post=3549961]post #8[/post] where nobody in their right mind would even begin trying to answer the question from the perspective of an inertial frame.

I doubt that that would be necessary in order to avoid using fictitious forces; but that's what is to be seen! So, instead of continuing with making assertions that cannot be tested, please provide just one detailed calculation example using fictitious force that we can put to the test - that's the purpose of this thread.

 

[D H]

Right - it's an improper use of Newton's laws, misapplying them with respect to rotating frames.

There is no misapplying here. All frames of reference are equally valid. You just have to do the math right.

However, the point of this thread is to put the claim to the test that this improper utilisation is very useful, or even necessary to solve certain problems. And regretfully, so far not a single calculation example with fictitious forces of such a case has been given... Thus the challenge remains open to those who made such claims.

Oh, please. I gave several examples. All you have to do is google those terms. You will find web pages, journal articles, even books on the cited subject. You want a simple example. Such a simple example doesn't exist. If it was just one simple equation there would be no reason to add the complexity of fictitious forces. Fictitious forces vanish in an inertial frame. We add that complexity because there is a whole lot more than one simple equation is involved in those applications.

This is very basic sophomore/junior level physics. It is downright silly to be arguing about it.

 

[harrylin]

There is no misapplying here. All frames of reference are equally valid. You just have to do the math right.

Same as when you apply the Lorentz transformations to accelerating frames: that is misapplication by definition. And of course you can always improvise to make it kind of work outside of the specs (as you say, "just ... do the math right").

Oh, please. I gave several examples. All you have to do is google those terms. You will find web pages, journal articles, even books on the cited subject. You want a simple example. Such a simple example doesn't exist. [..] This is very basic sophomore/junior level physics. It is downright silly to be arguing about it.

Again: this has nothing to do with basic level physic. The purpose here is to avoid arguing with words (that's useless!) and stick to calculations instead. If you know of no simple calculation example, then please provide a link to a complicated one that you think makes your point.

Harald

 

[A.T.]

And of course you can always improvise to make it kind of work

What do you mean by "improvise"? The point of having the concept of inertial forces is that you don't have to improvise, and derive ad-hoc corrections for each non-inertial frame case. Instead you apply a consistent set of rules to get the correct results. And it doesn't just "kind of work". It works perfectly. It is not more of an "improvisation" than Newton's unmodified laws.

 

[Dale]

Develop the equations of motion for a satellite in a Lissajous orbit about the sun-earth L1 point.

If you know of no simple calculation example, then please provide a link to a complicated one that you think makes your point.

http://www.cds.caltech.edu/archive/help/uploads/wiki/files/39/lecture_halo_2004.pdf

 

[harrylin]

http://www.cds.caltech.edu/archive/help/uploads/wiki/files/39/lecture_halo_2004.pdf

Thanks! But did you give this to demonstrate that fictitious forces are not necessary? Because no such forces are used there, as far as I can see.

 

[D H]

Thanks! But did you give this to demonstrate that fictitious forces are not necessary?

Nobody has said that fictitious forces are necessary. It is just that in some cases the problem becomes intractable or overly complex without the use of such devices.

Because no such forces are used there, as far as I can see.

Sure they are. Slide #2 starts with "Recall equations of CR3BP" and then presents the equations of motion for this system. Those equations of motion are those of a spacecraft (labeled S/C in the figure) expressed in a rotating frame of reference.

Some background: CR3BP (some use CRTBP) is short for "circular restricted 3 body problem" (or "circular restricted three body problem" in the case of CRTBP). I strongly suggest you google those two phrases.

The subject of the CR3BP is the motion of a very, very small third body in the presence of a pair of bodies in circular orbits about their center of mass. (The more general problem of the elliptical restricted 3 body problem is a much tougher nut to crack.) Of the two massive bodies, one will be more massive than the other. This larger body is called the primary body, the smaller one, the secondary body. Restricting the third body to having a mass that is many, many orders of magnitude smaller than that of the secondary means that the effect of the third body on the behaviors of the primary and secondary bodies will be negligible and can be ignored.

Those equations of motion are not expressed in SI units. They are instead expressed in units such that

• One mass unit is the sum of the masses of the primary and secondary bodies. In these units, the secondary body has mass μ; the primary body has mass 1-μ. The primary is by definition the more massive of the two bodies, meaning that μ is between 0 and 1/2.
• One distance unit is the distance between the primary and secondary bodies. This distance is constant since the primary and secondary a two bodies are in circular orbits about one another.
• One time unit is the orbital period the primary and secondary bodies divided by (2*pi).

Note that, by definition, this system of units yields numeric values of one for the total mass of the system and for the orbital radius. A couple of other key quantities also have a numeric value of one in this system of units. These are the universal gravitational constant G and the magnitude of the primary and secondary's angular velocity vector ω.

Working in inertial coordinates would yield nine coupled, non-linear second order differential equations: An absolute mess. Switching to a frame that is rotating with the orbit of the primary and secondary about their center of mass simplifies things immensely. The primary and secondary are not moving in this frame. Six of those nine coupled, non-linear second order differential equations just vanish. The three equations of motion that remain describe the body of interest, the third body. Those three equations of motion now include terms due to the fictitious centrifugal acceleration, but this is a very small price to pay for having six of the original equations of motion just vanish.

 

[harrylin]

[..] Sure [fictitious forces] are [used there]. Slide #2 starts with "Recall equations of CR3BP" and then presents the equations of motion for this system. Those equations of motion are those of a spacecraft (labeled S/C in the figure) expressed in a rotating frame of reference.

Some background: CR3BP (some use CRTBP) is short for "circular restricted 3 body problem" (or "circular restricted three body problem" in the case of CRTBP). I strongly suggest you google those two phrases.

OK - so you claim that fictitious forces were used to derive those equations. Slowly we are getting somewhere.

Now we only have to find a presentation of such a derivation with fictitious forces, and which we can then compare with the equivalent derivation without such forces, if it's practically doable.

So, checked with Google and found for example:
http://www.cdeagle.com/ommatlab/crtbp.pdf
However, again I noticed no reference to fictitious forces!

The subject of the CR3BP is the motion of a very, very small third body in the presence of a pair of bodies in circular orbits about their center of mass. (The more general problem of the elliptical restricted 3 body problem is a much tougher nut to crack.) Of the two massive bodies, one will be more massive than the other. This larger body is called the primary body, the smaller one, the secondary body. Restricting the third body to having a mass that is many, many orders of magnitude smaller than that of the secondary means that the effect of the third body on the behaviors of the primary and secondary bodies will be negligible and can be ignored.

Those equations of motion are not expressed in SI units. They are instead expressed in units such that

• One mass unit is the sum of the masses of the primary and secondary bodies. In these units, the secondary body has mass μ; the primary body has mass 1-μ. The primary is by definition the more massive of the two bodies, meaning that μ is between 0 and 1/2.
• One distance unit is the distance between the primary and secondary bodies. This distance is constant since the primary and secondary a two bodies are in circular orbits about one another.
• One time unit is the orbital period the primary and secondary bodies divided by (2*pi).

Note that, by definition, this system of units yields numeric values of one for the total mass of the system and for the orbital radius. A couple of other key quantities also have a numeric value of one in this system of units. These are the universal gravitational constant G and the magnitude of the primary and secondary's angular velocity vector ω.

Thanks for the clarification.

Working in inertial coordinates would yield nine coupled, non-linear second order differential equations: An absolute mess. Switching to a frame that is rotating with the orbit of the primary and secondary about their center of mass simplifies things immensely.

I fully agree; and that was never an issue. It's a common misconception to think that one has to use fictitious forces in order to map equations of motion to a rotating frame.

The primary and secondary are not moving in this frame. Six of those nine coupled, non-linear second order differential equations just vanish. The three equations of motion that remain describe the body of interest, the third body. Those three equations of motion now include terms due to the fictitious centrifugal acceleration, but this is a very small price to pay for having six of the original equations of motion just vanish.

Coordinate acceleration should not be confounded with fictitious force - those are unrelated concepts. And I did not spot a fictitious force in the derivation above.Harald

 

[D H]

Coordinate acceleration should not be confounded with fictitious force - those are unrelated concepts. And I did not spot a fictitious force in the derivation above.

There you go then. This is the source of your confusion. In Newtonian mechanics, coordinate acceleration and fictitious forces are essentially same thing, sans a factor of mass. The net fictitious force is simply coordinate acceleration times mass.

 

[Dale]

It's a common misconception to think that one has to use fictitious forces in order to map equations of motion to a rotating frame.

This is not correct. One does have to use ficititious forces in a rotating frame, otherwise the equations of motion are incorrect.

What one does not have to do is to stick a big label on them and say "this term here is a fictitious force". The appropriate terms in the equations of motion represent fictitious forces whether or not they are explicitly labeled as such.

 

[Dale]

In Newtonian mechanics, coordinate acceleration and fictitious forces are essentially same thing, sans a factor of mass.

To further emphasize this point, fictitious forces are always proportional to mass, so you can always drop or add a factor of mass to go between the two.

 

[harrylin]

There you go then. This is the source of your confusion. In Newtonian mechanics, coordinate acceleration and fictitious forces are essentially same thing, sans a factor of mass. The net fictitious force is simply coordinate acceleration times mass.

You mean your confusion.
But indeed, this seems to be largely a matter of words! In Newtonian mechanics as well as most textbooks (including the one that you directed me to by means of Google), coordinate acceleration exists due to Newtonian ("real") forces, and no fictitious force concepts are introduced at all.

[..]What one does not have to do is to stick a big label on them and say "this term here is a fictitious force". The appropriate terms in the equations of motion represent fictitious forces whether or not they are explicitly labeled as such.

What you call "fictitious force", others might call an artifact or correction term for non-inertial motion; and although mathematically the value will be the same, conceptually that is very different. So, it's not merely a matter of labels, but also of concepts. Perhaps that is why some teachers can get very upset when others call those correction terms "fictitious forces".

Anyway, as commonly textbooks do not use the fictitious force concept for those derivations, I take it that my question has been sufficiently answered.

Thanks for the feedback!

 

[A.T.]

coordinate acceleration exists due to Newtonian ("real") forces, and no fictitious force concepts are introduced at all.

In general coordinate acceleration depends on the net force, which is the sum of all forces that might act: interaction and inertial.

 

[Dale]

What you call "fictitious force", others might call an artifact or correction term for non-inertial motion; and although mathematically the value will be the same, conceptually that is very different. So, it's not merely a matter of labels, but also of concepts. Perhaps that is why some teachers can get very upset when others call those correction terms "fictitious forces".

It doesn't matter if you also call it an "artifact" or a "correction term" or "Bob's uncle". It fits the definition of a fictitious force therefore it is a fictitious force, regardless of what other definitions it also fits.

Your argument here is like saying that a square is not a rectangle because other people will call it a square, and it isn't just a matter of labels since squares and rectangles are conceptually different, and some people get upset if you call a square a rectangle. It is an invalid argument. A square is a rectangle because it fits the definition of a rectangle, and the extra terms in the equations of motion in a non-inertial frame are fictitious forces because they fit the definition of a fictitious force.

Anyway, as commonly textbooks do not use the fictitious force concept for those derivations, I take it that my question has been sufficiently answered.

Kindly back up this claim with a reference. All textbooks should use fictitious forces, either as a part of the derivation or as an end result of the derivation. If they do not, then they are in error. Obviously, they may not discuss their use of fictitious forces, but they must use them.

 

[harrylin]

[..]
Kindly back up this claim with a reference. All textbooks should use fictitious forces, either as a part of the derivation or as an end result of the derivation. If they do not, then they are in error. Obviously, they may not discuss their use of fictitious forces, but they must use them.

Already given and commented in post #65; similar to basic textbooks that discuss Coriolis acceleration etc. without introducing the fictitious force concept. It was in that sense that I intended my question, which now has been answered to my satisfaction.

 

[D H]

Already given and commented in post #65; similar to basic textbooks that discuss Coriolis acceleration etc. without introducing the fictitious force concept. It was in that sense that I intended my question, which now has been answered to my satisfaction.

Coriolis acceleration and coriolis force are one and the same thing, sans a factor of mass. You are playing a stupid semantics game, Harald.

Thread closed.