Are fictitious forces necessary to solve certain problems?

[harrylin]

It can be handy to ignore the Earth's rotation and simply work with the effective g', instead of accounting for g'=g+a; and similarly it may be handy to use Coriolis forces and so on for weather predictions. Nevertheless I assume that calculations with fictitious forces can always be reconverted in similar calculations without them, for the simple reason that they are based on Newtonian physics that does without them.

However, in recent discussions*, several people asserted that for particular cases it is necessary to introduce fictitious forces, or at least that introducing them significantly simplifies calculations of particular problems.

I invite those who agree with such claims to give specific examples here. Then we can put such claims to the test by trying to do similar calculations without fictitious forces.

*https://www.physicsforums.com/showthread.php?t=523212
https://www.physicsforums.com/showthread.php?t=536846

 

[A.T.]

or at least that introducing them significantly simplifies calculations of particular problems.

Yes it does. If all your inputs are given in some non-inertial frame, and you need the results also in that frame, then what is the point in using some inertial frame for the calculation?

 

[Hootenanny]

Nevertheless I assume that calculations with fictitious forces can always be reconverted in similar calculations without them

I have to disagree with you there.

I invite those who agree with such claims to give specific examples here. Then we can put such claims to the test by trying to do similar calculations without fictitious forces.

Very well. I'll let you offer your solution to the following question without referencing fictitious forces.

A rabbit of mass 1kg is sat still at the very edge of a circular roundabout, which has a radius of 1m. The roundabout is rotating at 1 rad/s. Compute the net force acting on the rabbit from the rabbit's point of view.​

 

[mikeph]

A rabbit of mass 1kg is sat still at the very edge of a circular roundabout, which has a radius of 1m. The roundabout is rotating at 1 rad/s. Compute the net force acting on the rabbit from the rabbit's point of view.​

I would say that question is invalid because it depends subjectively on the rabbit's experience. In terms of objective, physical outcomes (eg. will the rabbit fall off or not), there would be no requirement for a non-inertial frame.

I tend to agree with the original poster. The only difference is the maths; our arbitrary choice of perspective cannot possibly affect the physics of the situation, because there is no causal connection between the problem itself and the person solving the problem.

 

[Hootenanny]

I would say that question is invalid because it depends subjectively on the rabbit's experience.

I don't quite understand - if you are referring to the rabbit's "conciousness", then simply replace rabbit by particle.

In terms of objective, physical outcomes (eg. will the rabbit fall off or not), there would be no requirement for a non-inertial frame.

I didn't ask about physical outcomes. I explicitly asked harry to compute the net force in a non-inertial frame. There is no way to do this without moving to the frame in question.

 

[mikeph]

I didn't ask about physical outcomes.

The force "felt" by a particle can be disputed by different observers but the motion of that particle cannot be disputed, so I think you are giving a "trivial" solution to the problem and that OP's question should be re-worded.

Can you give me a physical scenario where it is not possible to predict the state of a system at a later time unless fictitious forces are used?

 

[harrylin]

I have to disagree with you there.

Very well. I'll let you offer your solution to the following question without referencing fictitious forces.

A rabbit of mass 1kg is sat still at the very edge of a circular roundabout, which has a radius of 1m. The roundabout is rotating at 1 rad/s. Compute the net force acting on the rabbit from the rabbit's point of view.​

The point is to verify that your solution cannot be rewritten without fictitious forces, or at least, not without extremely complicating the calculation. Remember, I'm not making the claims here; but I'm willing to put your solution to the test.

PS: calculating the force that a rotating rabbit will measure is very basic Newtonian mechanics; D_H suggested that it becomes problematic for much more complex systems

 

[D H]

Nevertheless I assume that calculations with fictitious forces can always be reconverted in similar calculations without them, for the simple reason that they are based on Newtonian physics that does without them.

The simple Newtonian physics that one does at the high school and freshman level in college does without inertial forces and torques. More advanced physics does not.

However, in recent discussions*, several people asserted that for particular cases it is necessary to introduce fictitious forces, or at least that introducing them significantly simplifies calculations of particular problems.

Nobody has said that in theory one could not solve such systems without the use of inertial forces and torques. In practice, there are many places where it is foolhardy (at best) to avoid the use of such devices.

I invite those who agree with such claims to give specific examples here. Then we can put such claims to the test by trying to do similar calculations without fictitious forces.

1. A simple one to start with: Compute the forces due to the moon and the sun on a particle on the surface of the Earth relative to the Earth as a whole. This is easy to do in inertial and accelerating coordinates, but it serves as a nice starter.
2. This one is a bit tougher: Model the weather to the extent that you can predict the landfall of a hurricane or the likelihood of a tornado outbreak with some reasonable semblance of accuracy.
3. Even tougher: Model the effects on a hurricane as the hurricane passes over a set of mountainous islands in the Caribbean.
4. Simpler again: Pick up a book, preferably a hardcover book. Put a rubber band around the book so it won't fly open during the course of the experiment. Hold the book in one hand at the center of the bottom edge, with the cover of the book horizontal and facing upward and the spine of the book to the left. Toss the book upward, giving it a flip as you do so. Explain the motion of the book.
5. Same problem, but more generic: Explain why "the polhode rolls without slipping on the herpolhode lying in the invariable plane."
6. Problem #4 again, but this time with a softcover book given a flip out in space. The book will eventually stabilize to rotating about the axis normal to the cover of the book. Why? (Hint: It is well-known that rotations about the principal axes with the least and greatest moments of inertia are stable in the case of a rigid body. It is less well-known that there is only one stable axis of rotation, a rotation about the principal axis with the greatest moment of inertia, for a non-rigid body. Why?)
7. Develop the equations of motion for an articulated robot with three or more joints whose links are rigid bodies.
8. Develop the equations of motion for an articulated robot with three or more joints whose links are flexible bodies.
9. Develop the equations of motion for a satellite in a Lissajous orbit about the sun-earth L1 point.

 

[harrylin]

[..] OP's question should be re-worded.

Can you give me a physical scenario where it is not possible to predict the state of a system at a later time unless fictitious forces are used?

Sorry if my question was ambiguous (can you explain in what way?). Your rephrasing does match my question; however I also allow for the weaker claim about complexity, which I would like to put it to the test by comparing the lengths of the calculations.

 

[Studiot]

In this recent thread I offered a problem (posts 53 and 54) where D'Alembert's method (fictious forces) will definitely get you the wrong answer.

https://www.physicsforums.com/showthread.php?t=531470

 

[A.T.]

In this recent thread I offered a problem (posts 53 and 54) where D'Alembert's method (fictious forces) will definitely get you the wrong answer.

https://www.physicsforums.com/showthread.php?t=531470

What makes you think so?

 

[A.T.]

Can you give me a physical scenario where it is not possible to predict the state of a system at a later time unless fictitious forces are used?

Has anyone actually made that claim?

 

[D H]

In this recent thread I offered a problem (posts 53 and 54) where D'Alembert's method (fictious forces) will definitely get you the wrong answer.

https://www.physicsforums.com/showthread.php?t=531470

No, you didn't.

All frames of reference are equally valid. Formulate the problem correctly and avoid errors along the way to the soluation and you will come up with the same answer regardless of the reference frames you use to solve the problem. If you formulate the problem incorrectly or make some mistake along the way, all you have demonstrated is that somewhere you made a mistake.

While all frames of reference are equally valid, for a given problem, some frames of reference are a lot easier to work with, are less likely to induce to human errors, and are less likely to induce mathematical errors such as caused by using finite precision arithmetic (e.g., a calculator or a computer that uses an IEEE floating point representation).

 

[mikeph]

Sorry if my question was ambiguous (can you explain in what way?). Your rephrasing does match my question; however I also allow for the weaker claim about complexity, which I would like to put it to the test by comparing the lengths of the calculations.

It wasn't ambiguous but I got the sense that it permitted solutions which did not match what you were seeking (such as "what forces are felt by a rabbit...").

My understanding is that inertial forces are never required to solve physical problems that are not specifically asking "what is the inertial force that is felt by...". Nobody is forcing you to use a rotating coordinate system, because the choice of coordinates does not affect the motion of a particle in reality (it necessarily cannot and if it does, there is an error somewhere).

I did some work on the three body problem and I can guarantee that a rotating frame will make things far easier, because it does, in a sense, eliminate much of the time-dependence of the bodies' positions. In a suitable frame, the Earth and the Sun are both at rest, and a third body (say, the moon) will have certain motions that you can analyse. Without this rotating frame, things get very very complicated very quickly. But I would not say that they get impossible.

 

[D H]

Can you give me a physical scenario where it is not possible to predict the state of a system at a later time unless fictitious forces are used?

Has anyone actually made that claim?

No one has made such a claim that I have seen.

I did some work on the three body problem and I can guarantee that a rotating frame will make things far easier, because it does, in a sense, eliminate much of the time-dependence of the bodies' positions.

Yep. This is my problem #9 in [post=3549961]this post[/post].

 

[Studiot]

All frames of reference are equally valid.

I didn't say they weren't.

No, you didn't.

No one has yet offered a correct answer to the question I asked.

Formulate the problem correctly

Di you mean formulate the problem or formulate a solution?

I formulated the problem correctly, if you can allow me the faux pas of missing out part of the information in the first post, information that was supplied in the second.

 

[A.T.]

No one has yet offered a correct answer to the question I asked.I formulated the problem correctly, if you can allow me the faux pas of missing out part of the information in the first post, information that was supplied in the second.

Why don't you write again the complete question in one post, give us your two solutions (inertial frame, co-rotating frame with fictious forces) and show us how the later "will definitely get you the wrong answer"?

Edit by DH:
Please take this discussion to Studiot's thread, [thread]531470[/thread]. Here it just serves as a way to drag the discussion off-topic.

 

[Dale]

In this recent thread I offered a problem (posts 53 and 54) where D'Alembert's method (fictious forces) will definitely get you the wrong answer.

https://www.physicsforums.com/showthread.php?t=531470

Fictitious forces will never get you the wrong answer unless you make a mistake.

 

[Dale]

A rabbit of mass 1kg is sat still at the very edge of a circular roundabout, which has a radius of 1m. The roundabout is rotating at 1 rad/s. Compute the net force acting on the rabbit from the rabbit's point of view.​

Well, that is zero by definition of "the rabbit's point of view", so there is no need to actually calculate any fictitious forces. You would be better off asking for the force on a different object from the rabbit's point of view. Or asking for all of the forces rather than just the net force.

 

[Hootenanny]

Well, that is zero by definition of "the rabbit's point of view", so there is no need to actually calculate any fictitious forces. You would be better off asking for the force on a different object from the rabbit's point of view. Or asking for all of the forces rather than just the net force.

I know. I was trying to eliminate as much computation as possible from the question so that the central point does not get obfuscated, as it has been in previous threads. The point is that if you are asked for a quantity in a non-inertial frame, you have no choice but to work with fictitious forces.

Perhaps you a right, I should have asked for a specific force acting on the rabbit. However, the point still remains: if you fail to account for the fictitious centrifugal force acting on the rabbit, then then net force will not vanish.

 

[Hootenanny]

The force "felt" by a particle can be disputed by different observers but the motion of that particle cannot be disputed, so I think you are giving a "trivial" solution to the problem and that OP's question should be re-worded.

The problem whilst trivial, requires the acknowledgment of the fictitious force present in the particle's frame. As I said above, I intentionally gave a trivial example in order to avoid confusion.

Can you give me a physical scenario where it is not possible to predict the state of a system at a later time unless fictitious forces are used?

No, I cannot. Since one can always transform to an inertial reference frame, it is always possible to carry out computations without reference to pseudo-forces. However, if you need the answer in a non-inertial frame, pseudo-forces will appear when to transform to the non-inertial frame. There's no getting away from it.

 

[Dale]

However, the point still remains: if you fail to account for the fictitious centrifugal force acting on the rabbit, then then net force will not vanish.

Agreed, and I understand your pedagogical point also.

 

[D H]

Can you give me a physical scenario where it is not possible to predict the state of a system at a later time unless fictitious forces are used?

This is a fallacious line of reasoning; it is a red herring. This is fallacious because nobody other than you the OP and you has made such a claim. I suggest (no, as a moderator, I insist) that this line of reasoning be dropped.

People use non-inertial frames for a number of reasons, but that it is impossible to predict the state of a system without the use of a non-inertial frame is not one of them. We use non-inertial frames because

• Their use makes the calculations at hand take on a much simpler form;
• Their use makes the numerical calculations more stable, more accurate (e.g., one doesn't have to resort to infinite precision arithmetic to compute the answer);
• The question requires that the answer be expressed in some non-inertial frame;
• And others. The above list is not exhaustive.

Besides, what inertial frame? Every reference frame we can construct is a non-inertial frame. As one of my bosses said to me long ago, "If you think there is such a thing as an inertial frame, name one."

 

[mikeph]

I don't understand why you disagree with me since everything you have just said, I agree with. Why is it a fallacicous line of reasoning when it very closely follow's the original poster's question, and the person whom I quoted replied to me saying "I agree with you".

I don't know what claim that I apparently made that you're referring to either. I never said ficticious forces are NECESSARY, in fact everything I've written is arguing against this, as you've just done.

 

[Hootenanny]

I don't understand why you disagree with me since everything you have just said, I agree with. Why is it a fallacicous line of reasoning when it very closely follow's the original poster's question, and the person whom I quoted replied to me saying "I agree with you".

I don't know what claim that I apparently made that you're referring to either. I never said ficticious forces are NECESSARY, in fact everything I've written is arguing against this, as you've just done.

Now you are playing word games.

I did not agree with you. I merely admitted that one can always use inertial frames to describe the state of a system. The question I quoted was not a statement and therefore I couldn't agree with it!

 

[mikeph]

Ok but your comment was in agreement with mine, although you did not quote that part.

 

[harrylin]

[..] Nobody has said that in theory one could not solve such systems without the use of inertial forces and torques.

Evidently you don't follow everything that everyone claims on physicsforums. See for example the claim in post #72 of https://www.physicsforums.com/showthread.php?t=523212 :
"You have to use the fictitious forces in the rotating frame, otherwise you get the wrong trajectory. It doesn't matter if you do your dynamics in the inertial frame and then transform the result to the rotating frame or if you do your dynamics in the rotating frame directly. Either way the trajectory in the rotating frame has coordinate accelerations that are not attributable to the real forces and require fictitious forces to explain."

In practice, there are many places where it is foolhardy (at best) to avoid the use of such devices.

1. A simple one to start with: Compute the forces due to the moon and the sun on a particle on the surface of the Earth relative to the Earth as a whole. This is easy to do in inertial and accelerating coordinates, but it serves as a nice starter.
2. This one is a bit tougher: Model the weather to the extent that you can predict the landfall of a hurricane or the likelihood of a tornado outbreak with some reasonable semblance of accuracy.
3. Even tougher: Model the effects on a hurricane as the hurricane passes over a set of mountainous islands in the Caribbean. [..]

One of them will do! Just provide a calculation with the use of fictitious forces and which you assume will be much more complicated without them. That will be enough to convince me (and most others), if we cannot provide an equivalent that is nearly as simple.

 

[harrylin]

[..] I should have asked for a specific force acting on the rabbit. However, the point still remains: if you fail to account for the fictitious centrifugal force acting on the rabbit, then then net force will not vanish.

Do you seriously think that it is impossible to calculate the force that the rabbit will measure (for example with a scale), without introducing a fictitious force in the calculation??

 

[A.T.]

Evidently you don't follow everything that everyone claims on physicsforums. See for example the claim in post #72 of https://www.physicsforums.com/showthread.php?t=523212 :
"You have to use the fictitious forces in the rotating frame, otherwise you get the wrong trajectory.

This just says that you have to use fictitious forces, when doing calculations in the rotating frame. This is different from claiming that "fictitious forces necessary to solve certain problems", unless the problem specifically asks about forces in the rotating frame (like Hootenanny'S example).

 

[harrylin]

This just says that you have to use fictitious forces, when doing calculations in the rotating frame. This is different from claiming that "fictitious forces necessary to solve certain problems", unless the problem specifically asks about forces in the rotating frame (like Hootenanny'S example).

The claim that I cited (of which you only retained a snippet) was that without using fictitious forces you even get an erroneous result if you do your dynamics in the inertial frame and then transform the result to the rotating frame. And that is simply wrong: one only needs to introduce fictitious forces if one fails to account for the fact that that frame is rotating. Compare for example GPS (no forces in GPS, but it's the same inertial frame approach).

Please let me remind you: the purpose of this thread is to verify to what extent we can match calculation examples with "necessary" fictitious forces by similar calculations without such forces. There is no issue with calculating the force that the rabbit feels, as it is only possible to feel a real force and it's a very simple problem; it looks to me that the real challenge is coming from D_H and I hope that he has a detailed example ready.

 

[A.T.]

[*]Model the weather to the extent that you can predict the landfall of a hurricane or the likelihood of a tornado outbreak with some reasonable semblance of accuracy.

A similar but simpler example is mesh based computational fluid dynamics for a rotating part (propeller. turbine, etc). In the non rotating frame the fluid volume has to be remeshed in each step, because the part moves. This is computationally very expensive. In the co-rotating frame the fluid spins, while the part & volume mesh are static. The CFD equations are simply modified by the inertial force terms.

I don't even want to start to imagine modelling weather in an inertial frame, that doesn't rotate with the Earth.

 

[harrylin]

A similar but simpler example is mesh based computational fluid dynamics for a rotating part (propeller. turbine, etc). In the non rotating frame the fluid volume has to be remeshed in each step, because the part moves. This is computationally very expensive. In the co-rotating frame the fluid spins, while the part & volume mesh are static. The CFD equations are simply modified by the inertial force terms.

I don't even want to start to imagine modelling weather in an inertial frame, that doesn't rotate with the Earth.

That sounds plausible. Anyway, the purpose here is to put such generic claims to the test. And different from your post #17 where you ask the claimant to provide both calculations, with and without fictitious force, I only ask for a single calculation example with fictitious force.

 

[A.T.]

The claim that I cited (of which you only retained a snippet) was that without using fictitious forces you even get an erroneous result if you do your dynamics in the inertial frame and then transform the result to the rotating frame

No. That is not what it says. Here is the quote again. I bolded the parts, that you keep ignoring:

"You have to use the fictitious forces in the rotating frame, otherwise you get the wrong trajectory. It doesn't matter if you do your dynamics in the inertial frame and then transform the result to the rotating frame or if you do your dynamics in the rotating frame directly. Either way the trajectory in the rotating frame has coordinate accelerations that are not attributable to the real forces and require fictitious forces to explain."

It specifically says that you can use both frames. But the coordinate accelerations measured in rotating frame can only be attributed to inertial forces.

 

[harrylin]

No. That is not what it says. Here is the quote again. I bolded the parts, that you keep ignoring:

It specifically says that you can use both frames. But the coordinate accelerations measured in rotating frame can only be attributed to inertial forces.

I already highlighted the parts that you keep ignoring; the bold parts do not change them. The coordinate accelerations can be attributed to the rotation of the frame, just as Newton did and GPS does.

But I let myself be side-tracked: all this talking in the air is contrary to the purpose of this thread. I asked for a calculation example with fictitious forces that we can put to the test; if you don't have one, please abstain from responding.

 

[A.T.]

The coordinate accelerations can be attributed to the rotation of the frame,

Only in trivial cases with no other forces acting. Inertial forces account for the non-inertial frame in a more general way that allows to combine them with interaction forces. The coordinate acceleration is the result of the net force, which in general is the sum of both: interaction and inertial forces.