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Mentor note:
Please keep future side discussions on Studiot's problem in [thread=531470]Studiot's thread[/thread].
Please keep future side discussions on Studiot's problem in [thread=531470]Studiot's thread[/thread].
Exactly. Weather models are essentially big CFD models. I couldn't imagine doing CFD with a movable mesh. What a mess!A.T. said:I don't even want to start to imagine modelling weather in an inertial frame, that doesn't rotate with the Earth.
Test what?harrylin said:Thanks for the clarifications! Although it does sound plausible, so far nobody has provided a calculation example that we can put to test.
A.T. said:Test what?
Hootenanny said: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 still remains: if you fail to account for the fictitious centrifugal force acting on the rabbit, then then net force will not vanish.
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.
D H said:Nobody has said that in theory one could not solve such systems without the use of inertial forces and torques.
Nevertheless I assume that calculations with fictitious forces can always be reconverted in similar calculations without them
Hootenanny said:I have to disagree with you there.
If net forces where the same, the acceleration would be the same. "Perception of the acceleration" is vague gibberish. Do you mean "coordinate acceleration"?cmb said:So, the net forces observed are the same. It is the perception of the acceleration that is different,
But I don't want to expect anything. The whole point of inertial forces is being able to assume F_net = m * a, just as if it was an inertial frame.cmb said:just as you would expect between a non- and an accelerating frame.
A.T. said:If net forces where the same, the acceleration would be the same. "Perception of the acceleration" is vague gibberish. Do you mean "coordinate acceleration"?
But I don't want to expect anything. The whole point of inertial forces is being able to assume F_net = m * a, just as if it was an inertial frame.just as you would expect between a non- and an accelerating frame.
What is "perceived acceleration"?cmb said:...perceived acceleration...
"Proper acceleration" is frame invariant. "Coordinate acceleration" is frame-dependent. The concept of inertial forces allows to use Newtons 2nd Law, in respect to coordinate acceleration.cmb said:It is the same acceleration, but how you describe that acceleration is frame-dependent.
It's not bad at all.cmb said:Too bad!
No, it isn't. In Newtonian mechanics, the acceleration of some object will be the same in all inertial frames. Allow non-inertial frames and acceleration is no longer frame invariant. A simple example: The acceleration of a helicopter hovering over some point on the surface of the Earth is identically zero from the perspective of a frame rotating with the Earth but is non-zero from the perspective of an inertial frame.cmb said:\It is the same acceleration, but how you describe that acceleration is frame-dependent.
A.T. said:What is "perceived acceleration"?
A.T. said:"Proper acceleration" is frame invariant. "Coordinate acceleration" is frame-dependent.
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.'A.T. said:The concept of inertial forces allows to use Newtons 2nd Law, in respect to coordinate acceleration.
D H said:No, it isn't. In Newtonian mechanics, the acceleration of some object will be the same in all inertial frames. Allow non-inertial frames and acceleration is no longer frame invariant. A simple example: The acceleration of a helicopter hovering over some point on the surface of the Earth is identically zero from the perspective of a frame rotating with the Earth but is non-zero from the perspective of an inertial frame.
Sure I can, if I assume inertial forces. The coordinate accelerarion in the rotating frame is proportional to the sum of all forces (interaction and inertial forces)A.T. said:You cannot claim to use the 2nd law (acceleration is proportional to force) if the whole framework of co-ordinates is, itself, rotating.
That might have been Newton's initial idea. But that concept was extended to non-inertial frames by others (d'Alembert, Corriolis etc.) by introducing inertial forces. The concept is still called Newton's 2nd Law even if it is more general than Newtons initial idea.A.T. said:Newton's 2nd law specifically refers to the notion of a linear function
Your point assumes that physics hasn't changed since Newton's time. It has. Your point is invalid.cmb said:My point that it is not right to both cite Newton and also claim 'non-inertial accelerations' in rotational frames.
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.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.
D H said: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.
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.cmb said: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.
Better said: There are no fictitious forces in an inertial frame.JeffKoch said: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".
Right - it's an improper use of Newton's laws, misapplying them with respect to rotating frames.cmb said:[..]
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!)
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 said:[..] 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.
There is no misapplying here. All frames of reference are equally valid. You just have to do the math right.harrylin said:Right - it's an improper use of Newton's laws, misapplying them with respect to rotating frames.
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.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.
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").D H said:There is no misapplying here. All frames of reference are equally valid. You just have to do the math right.
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.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.
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.harrylin said:And of course you can always improvise to make it kind of work
D H said:Develop the equations of motion for a satellite in a Lissajous orbit about the sun-earth L1 point.
http://www.cds.caltech.edu/archive/help/uploads/wiki/files/39/lecture_halo_2004.pdfharrylin said:If you know of no simple calculation example, then please provide a link to a complicated one that you think makes your point.
DaleSpam said:
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.harrylin said:Thanks! But did you give this to demonstrate that fictitious forces are not necessary?
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.Because no such forces are used there, as far as I can see.
OK - so you claim that fictitious forces were used to derive those equations. Slowly we are getting somewhere.D H said:[..] 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.
Thanks for the clarification.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.
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.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.
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.HaraldThe 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.
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.harrylin said: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.
This is not correct. One does have to use ficititious forces in a rotating frame, otherwise the equations of motion are incorrect.harrylin said: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.
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.D H said:In Newtonian mechanics, coordinate acceleration and fictitious forces are essentially same thing, sans a factor of mass.
D H said: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.
DaleSpam said:[..]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.
In general coordinate acceleration depends on the net force, which is the sum of all forces that might act: interaction and inertial.harrylin said:coordinate acceleration exists due to Newtonian ("real") forces, and no fictitious force concepts are introduced at all.