Dear Mr. Thierry De Mees!

I think that this = 1) a mechanical force between a translating object, in contact with a spinning object?

Yours faithfully, Ivan Ivanovich Dolgov 20180628 Д\д

Dear Thierry,

just an attempt: In a rotating reference system inertial trajectories as seen from a corrotating observer generally deviate from what they are expected to follow in the same system under non-rotating conditions. Devitions of the above type may be ascribed to virtual forces known as Coriolis forces.

Dear Ivan and Johan,

Thank you for your answers. However, both answers are very different.

Can there only be one right answer, i.e. is one of the answers wrong?

Best regards,

Thierry De Mees

"is one of the answers wrong?"

Dear Thierry,

I don't think so: The first answer relates to real contacting forces while the second one just considers free inertial trajectories and associated virtual forces. Contacting forces will occur whenever inertial trajectories are forced to stay in contact with some moving surface.

Dear Johan,

You wrote: "In a rotating reference system inertial trajectories as seen from a corrotating observer generally deviate from what they are expected to follow in the same system under non-rotating conditions."

Is it possible that a simple mathematical transform of coordinates would result in a force at all?

"is one of the answers wrong?"

How to combine them?

Best regards,

Thierry De Mees

"Is it possible that a simple mathematical transform of coordinates would result in a force at all?"

Dear Thierry,

in the 1970s I was concerned with some more complex type of Coriolis drag, see references below, which obviously confirm the basic mathematical procedure devised by James C. Keith.

Article Residual Drag Torque on Magnetically Suspended Rotating Spheres

Article Significant Deviation of Rotational Decay from Theory at a R...

https://nvlpubs.nist.gov/nistpubs/jres/67D/jresv67Dn5p533_A1b.pdf

Dear Johan,

If you don't mind, I would like to keep it simple and avoid external papers and links.

So, I reiterate the question, which is very important.

"Is it possible that a simple mathematical transform of coordinates would result in a force at all?"

Best regards,

Thierry De Mees

"Is it possible that a simple mathematical transform of coordinates would result in a force at all?"

Dear Thierry,

in accordance with Keith and associated experiments, as well as in view of meteorologic and other real phenomena, I think that real forces and dissipative drag should be expected only in case that inertial trajectories are forced to follow some predetermined path rather than by "simple mathematical transform of coordinates". As mentioned before, the latter at best will lead to virtual forces that might be considered in order to explain apparent aberrations of inertial trajectories.

I'm very curious to learn for what special reason you apparently ascribe some key significance to your present question in view of basic physics.

Dear Johan,

Thank you for your very concise answer. Since the Coriolis force is a very poorly known effect when scrutinizing the opinions on the internet, I am forced to go into detail in that.

You mention "simple mathematical transform of coordinates" as "at best will lead to virtual forces that might be considered in order to explain apparent aberrations of inertial trajectories."

That is very important.

So, the question is: can one invoke the Coriolis force if "apparent aberrations of inertial trajectories" are not caused by a mechanical contact between a translating object with a spinning object?

Best regards,

Thierry De Mees

Dear Thierry,

by "apparent aberrations of inertial trajectories" I mean those observed from the perspective of a rotating system, in particular, apparent bending of free inertial trajectories that are expected to be straight. The observer might be inclined to ascribe the apparent aberration to some kind of virtual deflection forces.

Thus "apparent aberrations of inertial trajectories" in the above sense are independent of mechanical contact and associated real forces.

Real forces come into play whenever a free inertial trajectory is forced on a prescribed path by force transmission via either mechanical contact or via non-contacting field transmission. The former mechanism leads to whirling weather formations on the earth's surface, while the latter has been thoroughly investigated in the rotational drag experiments mentioned above.

Thus Coriolis effects need not neccessarly be caused by mechanical contact.

Hello Thierry De Mees,

Your last point is very crucial....."are not caused by a mechanical contact between a translating object with a spinning object? " There is well and enough description about it in the book "Introduction to Classical Mechanics With Problems and Solutions, David Morin, Harvard University" which particularly focuses on the issue of frictional force to get impact measure of Coriolis force. But I think, if Newtonian kind of space is correct than we can't invoke it to be valid there as there will be no inter-space connection between two points in two different frames. Talking to Einstein's type, it might definitely be possible.

Within Newtonian type also, we may interpret differently. Like, if an Astranut is roaming in outer space of Earth with opening eyes, he could proclaim the presence of Coriolis effect but closing the eyes, I think he can't feel it. Actually, it is not physical. For example, let in ideal space if two observers are observing each other, and their motion is controlled by some outside source (say remoting system). If one come into motion, there will be apparent fictitious motion felt by the next observer if saw the receding of next observer but no difference if closes he eyes.

Dear Bishal,

Thank you for sharing the information about the book "Introduction to Classical Mechanics With Problems and Solutions, David Morin, Harvard University" which particularly focuses on the issue of frictional force to get impact measure of Coriolis force.

That corresponds with Ivan's point of view but is in strong contrast with Johan's "Thus Coriolis effects need not neccessarly be caused by mechanical contact."

Dear Johan,

You wrote : "by "apparent aberrations of inertial trajectories" I mean those observed from the perspective of a rotating system, in particular, apparent bending of free inertial trajectories that are expected to be straight. The observer might be inclined to ascribe the apparent aberration to some kind of virtual deflection forces."

So, I assume that you mean here the consequence of a coordinate transform, equally to what Bishal wrote: "closing the eyes, I think he can't feel it."

So, why would a simple coordinate transform be called "Coriolis force or effect" if it is just that?

Also, would anyone call the Harvard book being wrong?

Would the Coriolis not be (in the first place) a real force, by a physical contact?

Best regards,

Thierry De Mees

"So, why would a simple coordinate transform be called "Coriolis force or effect" if it is just that?"

Dear Thierry,

I think apparent as well as real effects as specifically observed on rotating systems are generally termed "Coriolis effects" which, in particular, includes Coriolis forces and drag.

Dear Johan,

Can we resume the whole question as follows, thanks to your above answer?

Let us indeed focus upon the two aspects of your answer:

1) Coriolis force

2) Coriolis effect

Historically, Gaspard-Gustave de Coriolis has found that the physical contact between a radially moving object upon a rotating device provides the moving object with an additional force, the Coriolis force, which equals to: m v x w in a co-rotating frame. (w is the angular velocity).

This force, which is real, and which is deviating the object in contact with the rotating device, as seen when co-rotating, is seen differently from a non-co-rotating observer.

The additional apparent effect of deviation is the Coriolis , which is also giving an extra m v x w when transforming from a co-rotating frame to a non-co-rotating (inertial) frame.

Hence, the resulting total deviation of the contact motion, as seen from the stationary observer is 2 m v x w.

However, if the first, physical contact-dependent Coriolis force doesn't appear in a given experiment, the second Coriolis effect cannot exist either, since in that case, there is only a coordinate transform of a non-deviated mass.

I am not sure that the strict separation of the two aspects of 1) and 2) as above, is usual. Maybe there has been a mixing up in literature as well.

With best regards,

Thierry De Mees

Dear Johan,

I have removed the link I had given in my last post, because it is an example of what the Coriolis is not, according to the principle of contact between the translating mass and the rotating device.

Indeed, in

https://sciencedemonstrations.fas.harvard.edu/presentations/coriolis-effect

the man throws a ball towards the basket. Hence, the ball obtains a radial velocity and on the other hand it is rotating, so, it has a tangential velocity equal to the outer velocity of the rotating device.

These both velocites remain constant, so, there is no force acting on it.

With the contact procedure on the other hand (the correct Coriolis force), there is a force F = m v x w, resulting in a sidewise acceleration or deceleration. The sidewise velocity will increase according to F = ma.

The additional rotation, as seen from the inertial frame, gives an additional apparent force F = m v x w, which will result in an additional apparent F = ma, due to the coordinate transform.

Continuing in this reasoning, the given link is only showing the part of the effect of rotation as a coordinate transform, and not the one of the contact procedure, as Coriolis historically found.

With best regards,

Thierry De Mees

"I am not sure that the strict separation of the two aspects of 1) and 2) as above, is usual."

Dear Thierry,

thanks for your careful analysis of phenomena occuring on rotating systems, as observed from inside and outside the rotating system, that possibly may all be treated under the label "Coriolis effects". Thanks, in particular, for referring to the original definition by Coriolis himself who obviously has focused on the contacting force as seen from the rotating system's perspective. I think it might be reasonable to regard the Coriolis force in its original appearance as a Coriolis effect of preferred practical significance on rotating systems, rather than treating it as something separate.

And the most bizarre and hilarious point is, it doesn't act along the direction of velocity.

Dear Bishal,

The reason why the force acts transversally can easily be explained by the following:

Imagine a number of parallel conveyor belts, like in airports, and the last conveyor belt is going faster than the forelast one, which is also faster than the next one, and so on. Let all the speed increments be identical.The speeds are v1 < v2 < v3 etc. The width of each conveyor is s.

Imagine that you can walk transversally over the conveyor belts with a velocity v.

Starting at the first one, you go sideways by a velocity v1.

Then, you step on the following one, which is a bit faster. Your inertia wants to keep the speed of the first conveyor belt, but your feet are now going at v2 > v1.

Hence, your feet are pulled sideways and you get a sideways acceleration.

While walking on the following conveyor belts, that effect continues.

The calculus of the force would be:

F = m v (vi - vi-1)/s

This is only half the Coriolis force as found for rotating devices ( F = 2 m v x w), and it is now clear why: the second half is given by the rotation itself, which makes the appearant force due to the rotation, as seen by a stationary observer: F = m v x w = m a.

With best regards,

Thierry De Mees

Hello Thierry,

I think you should not go so far. A simple example is watching the motion of sun from the earth surface assuming Sun to be stationary (not earth). The observation from the scaling of frame-dependence predicts a non-physical acceleration in out ward direction called Coriolis force.

Dear Bishal,

That is precisely the reason of my question. Why should a simple change of coordinate system be called a Coriolis force?

In the first place, there is no force but gravity, and the power of inertia in orbital physics.

Moreover, Gaspard-Gustave de Coriolis historically studied the case of contact between a translating mass upon a rotating device.

Finally, you mentioned yourself the book "Introduction to Classical Mechanics With Problems and Solutions, David Morin, Harvard University" which particularly focuses on the issue of frictional force to get impact measure of Coriolis force.

With best regards,

Thierry De Mees

Hello Thierry,

I don't know about the original paper but I mentioned what I learned. As I mentioned, there is only one difference that is closing or opening eyes in general. The way of including friction is quite odd because, the same form of formula fits for the observer inside aeroplane equally to the object falling from it. Regarding the form of formula and working mechanism, it is totally nonphysical.

Dear Bishal,

I am afraid that you mix up a number of things.

You are describing Kepler's orbitals, but attempt to change its name.

With best regards,

Thierry De Mees

Hello Thierry,

I think you are interpreting wrongly. Please read it once again. I don't mixed up every things but the usual description of existed form. And the above example is one of simple type that is widely mentioned. I think you mislead at the point of "falling" which I meant the falling of object radially downward where the Coriolis force acts tangentially to the path of aeroplane (use opposite Right hand rule). Refer the book I mentioned above.

Hi Bishal,

If an object is falling radially and without friction from an aeroplane, it will describe an elliptical path due to gravity.

Since one can assume the Earth being a point mass in Newtonian gravity with a good approximation, this elliptical path becomes a (almost) closed satellite path.

Nothing to do with the Coriolis force.

Best regards,

Thierry De Mees

Hello Thierry,

For an stationary observer resting on earth surface, he will see the motion parabolic not elliptical (to be elliptical the aeroplane must be in the velocity range of orbital velocity). To be clear what I mean't, see pg. 464-465 of that book.

Dear Bishal,

No, that is not correct. The trajectory is called parabolic because for simplicity, one assumed the Earth's gravity acceleration with height. In reality, it forms an elliptical orbit as long as the speed is below the escape velocity.

Best regards,

Thierry De Mees

Hello Thierry,

Will you mentioned the source, I am eager to see the result you described.

Dear Bishal,

In a hurry, I forgot the most important, which I corrected in my former post: the parabolic path assumes a constant gravity acceleration.

See:

https://www.scienceforums.net/topic/65664-free-fall-is-parabolic-or-elliptic/

Best regards,

Thierry De Mees

Dear Thierry,

According to the analysis of Landau & Lifshitz, Mechanics, page 128, rotation modifies the potential term in Lagrangian by adding a centrifugal correction and velocity-dependent Coriolis potential (equation 39.8). Coriolis effects seen from this perspective can be explained by the motion of a material point in this “combined” potential.

The situation becomes more complicated when you consider other forces that affect the system. Let's take a look at the Earth's atmosphere. The air parcels moving in the combined gravitational, centrifugal and Coriolis potential are subject to the action of other forces including pressure gradient and friction. The resulting motions are quite complicated, especially considering the role of the vertical component of the Coriolis force.

Dear Janusz,

Your post mentions quite a few things. Let's start with the beginning.

Rotation is: forcing masses to follow another path than the inertial, straight path. That's right.

But where is the Coriolis force when the Moon is orbiting about the Earth?

Best regards,

Thierry De Mees

Dear Sir,

Please also have a look at this useful link.

https://empslocal.ex.ac.uk/people/staff/gv219/classics.d/Persson98.pdf

Regards

The paper by Person is interesting and quite useful indeed. For some additional historical aspects of the Coriolis force please see:

http://www.bibnum.education.fr/sites/default/files/analyse-coriolis-force-en.pdf

To answer the question concerning the Moon please see the extremely informative and useful summary at:

http://www.afhalifax.ca/bete/DALEMBERTIMAGES/lune/gutzwiller-moon-earth-sin%20rmp.70.589.pdf

Dear Arvind,

Thanks for the link. Persson agrees with the fact that the Coriolis force is applicable when moving wrt the Earth's surface, although he doesn't firmly insist on it. However, he will not, ever, mention an alleged "floating" Coriolis force in the air, because that doesn't exist.

Dear Janusz,

Thanks for the links. The link wrt the Moon's orbit confirms that there is no Coriolis force for the Moon-Earth system. The only place where a Coriolis-like term (which is a totaly different thing) is indicated (with a negative sign), is when the Moon-Earth system is expressed in rotating coordinates of the Sun, as a three-body system.

Best regards,

Thierry De Mees

Thierry has here posed an intriguing question, especially since we are dealing with phenomena that influence direction of vertical and horizontal motion in both vertical and horizontal planes. His question points to a lacuna in the literature (of which I am aware), that is, the failure to define and reach a consensus of agreement on how to define the various phenomena to which the name of Coriolis has been attached.

Perhaps we would best consider that there may be a difference between how Coriolis himself would describe the phenomena he investigated and how scholars who specialize in this physics have described it. Herein I refer to the former as the “strict sense” of Coriolis as a phenomenal descriptor, and to the latter as the “broad sense”. Without citing sources, the avoidance of which was requested by the questioner, I can only record my impression that the name “Coriolis” has been attached to all of the consequences presently mentioned.

Of the first three choices in Thierry’s question, I lean to #2 (motion of an independent point in a rotating frame) as described by Ferrel’s Law and based on a thought experiment by Galileo; however, the Coriolis effect is perhaps more accurately and broadly #4 (something else), though it is a challenge to describe due to its diverse consequences: vertical deflection of horizontal motion such as Eotvos found in weighing eastbound versus westbound ships, horizontal deflection of vertical motion such as the early 19th century mineshaft-drop experiments measure as were predicted by Gauss and Laplace, and horizontal deflection of horizontal motion such as the inertial circular oscillations of sea water. Obviously I was neither born with any of this knowledge nor discovered it, but am otherwise complying with Thierry’s requested citation-avoidance.

As an early example of research into the horizontal component of this last phenomenon, while doing research for Galileo: His Science … [cf. my profile], I came across the said thought-experiment. As a consultant to Contarini at the Venetian arsenal, Galileo was of course concerned about where cannonballs would land under specified initial conditions and no atmospheric interference. He imagined the apparent deflection of an object moving along a longitude line or, to a lesser extent, moving in a direction that has a north-south component, which can be expected to deflect to the right in the northern hemisphere and to the left in the southern.

I suppose this happens because, as the projectile moves, it tends to retain the speed due to Earth’s rotation at the launch-point while the rotating Earth beneath alters its speed along the various latitude lines it crosses. To use one of Galileo’s examples, that of a projected cannonball, if fired to the north from the equator it would land somewhat east of the meridian on which it was fired. Due to the tangential velocity of a point on Earth varying with latitude the cannonball can be expected to travel eastward faster at the Equator than does its more northerly target or landing point. And mutatis mutandis for a cannonball fired to the South.

It thus seems that this Coriolis deflection can be attributed in part to Earth’s eastward rotation -- a phenomenon that Galileo strove mightily to demonstrate with many arguments – but which I do not see as having anything to do with “contact” or with “force”; hence I would refrain from any claim that these examples are “Coriolis” in the strict sense of his focus as Thierry described it. Nor would I argue against the notion that the Coriolis effects (in the broad sense) these examples demonstrate require no contact but can be described by mathematical transformations that calculate and predict measured deviations.

Dear all,

I got a nice description for the Coriolis force from Daniel Baldomir:

"The fictitious side force that seems to act on moving bodies in a rotating environment is called the Coriolis force, after the nineteenth-century French mathematician who first analyzed the effect. And the apparent acceleration of the sphere (it is a radial acceleration, not a tangential acceleration, in that only the direction changes, not the speed) is called the Coriolis acceleration. The entire effect is called the Coriolis effect."

The link is:

https://ocw.mit.edu/courses/earth-atmospheric-and-planetary-sciences/12-090-introduction-to-fluid-motions-sediment-transport-and-current-generated-sedimentary-structures-fall-2006/course-textbook/ch7.pdf

Best regards,

Thierry De Mees

I see it as a chief merit of Baldomir's description that it identifies the fictitious force as a radial acceleration. What that description seems to omit is motion -of an object longitudinally and at least partly under the influence of inertia acquired from a sphere, while it is no longer in contact with the sphere. In the absence of such an object in such motion, a rotating sphere would be accelerating everywhere but along its axis (i.e. at the poles) simply by virtue of the curvature of the sphere and consequent continuity in change of direction by every such point on the sphere. Is not the Coriolis effect described by Baldomir realized only in a second motion whose track recedes from one pole while approaching another?