Talk:Yaw, pitch, and roll: Difference between revisions
Corrections for consistency |
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== Corrections for consistency == |
== Corrections for consistency == |
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I'm about to edit the article to expand it and correct a mistake I made, hence my overwriting of my previous text here. If you read the previous entry (and current corrections to the article I made yesterday), I assumed that the article wanted to show the coordinates of the object once rotated by the yaw, pitch, roll, a bit like the picture shows. But I think it wanted to show the transform matrix from a coordinate system to a rotated one fixed to the plane, like I was actually constructing (a basis change.) So everything is applied in reverse: obviously, the true <math>R_{xyz}^{XYZ}</math> basis change is wrong right now, since it shows just the rotation. But of course a basis change is just the inverse of the transform applied to vectors to orient them like the new frame (but still in original frame coordinate). IE I just need the RHS being inverted to truly expressed the basis change <math>{xyz}->{XYZ}</math>. As it is, it rotates vectors keeping them expressed in the fixed coordinate system ''xyz''. Also, another thing that can get confusing for readers: sometimes on wiki, <math>R(\theta)</math> sometimes express just a rotation of vectors expressed in the same basis, but sometimes it expresses <math>R_b(\theta)=R(-\theta)</math>, the change of basis from the original basis to a rotated one. I will clarify this also. [[Special:Contributions/70.81.15.136|70.81.15.136]] ([[User talk:70.81.15.136|talk]]) 11:09, 11 June 2009 (UTC) |
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I have to agree with comments here (even as of today). Reading the article now I could pick serious inconsistencies, and it is very easy to mess things and totally confuse the reader on this subject. As a first example, note that the picture use a left handed coordinate system (then right handed). |
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Then we have this ("what were some thinking!?"): |
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<blockquote> |
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"Given this definition, the rotation sequence from xyz to XYZ is defined as follows: |
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<br /> |
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(Stevens, 26)<br /> |
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1. Right-handed rotation ψ about the z-axis by the yaw angle.<br /> |
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2. Right-handed rotation θ about the new (once-rotated) y-axis by the pitch angle.<br /> |
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3. Right-handed rotation φ about the new (twice-rotated) x-axis by the roll angle.<br /> |
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"</blockquote> |
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My comments: |
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#Be consistent: above it says LHVL (I know, a typo), then xyz, then in the equation "LHLV to XYZ", then right after "xyz to XYZ". |
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#Ok, for the rotations described, imagine a plane with wings parallel to the ground, nose pointing in the +x-axis, center of gravity at origin. The rotations above are stated relative to successively rotated frames so the successive rotations use as its axis of rotation one of the axis of the new frame each time: ie '''knowing already that''' <math>R_x(\theta)v</math> will rotate the column vector <math>v</math> around the x-axis of the basis on which <math>v</math> is expressed, the euclidean canonical one, thus around (1,0,0), if you want that rotation/x-axis to be anything else, then <math>v</math> would need to be expressed in that new basis before the rotation (which will now be relative to that new basis). |
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#By the previous point obviously you '''can't''' achieve the described rotations (and end result wanted) by doing:<br /> T := R<sub>''lhlv'' to ''XYZ''</sub> = ''R''<sub>''x''</sub>(roll) × ''R''<sub>''y''</sub>(pitch) × ''R''<sub>''z''</sub>(yaw) := <math>R_x(\varphi)R_y(\theta)R_z(\psi)</math><br /> and applying T to <math>v</math> (ie <math>Tv</math> isn't in the wanted orientation): <math>R_z(\psi)v</math> will surely get you in the correct yaw orientation, but then applying <math>R_y(\theta)</math> to the result (ie doing <math>R_y(\theta)R_z(\psi)v</math>) will not get you a pitch, but will change '''at the same time''' the yaw, pitch and roll of the plane, where the motion of the fuselage of the plane will describe a cone around the y-axis (ie the tip of <math>v</math> will make a circle orthogonal to the y-axis.)<br /> |
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#The only way applying <math>T</math> ''as is'' could work is if you did <math>(v^tT)=T^tv</math>, ie assume that the matrix is to be applied as a right-product to transform line vectors or just transpose it. But, first, the article never mentions that, and second, the text strongly implies that the matrix so described directly reflects the successive '''local''' rotations described in the 3 points paragraph above the equation, confusing further the careful reader and being obviously '''wrong'''. |
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::I said the article never mentioned that, more than that it clearly stated that <math>U_{XYZ}=TU{xyz}</math> where <math>U_{xyz}</math> is a column vector in basis ''xyz'', so it did assume column vectors and left multiplication after all. [[Special:Contributions/70.81.15.136|70.81.15.136]] ([[User talk:70.81.15.136|talk]]) 22:25, 10 June 2009 (UTC) |
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#As if it wasn't enough, the combined rotation matrix shows what seems to be the correct terms inside the matrix <math>T</math> described above, but the signs in many terms are wrong. The reason for that is yet (I presume) another copy-paste without thinking: Notice that everywhere the sign is switched, there is a multiplication of an odd number of sin() terms. Remember that the sin() function is an [[odd function]], <math>sin(-x)=-sin(x)</math>, and cos() is an even function, <math>cos(-x)=cos(x)</math>. Thus, it's as if the angle is reversed for every rotation, and this is equivalent to the z-axis being flipped (ie having a left handed coordinate system). Thus, the matrix as it currently is actually reflects a transform expressed in a ''left-handed coordinate system'' (with the z-axis inverted), actually consistent with the first picture (!) |
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#In summary, let us consider a right handed coordinate system, where a transform matrix is to left-multiply column vectors to apply the transform; let <math>\varphi</math> be the roll, <math>\theta</math> be the pitch and <math>\psi</math> be the yaw; the correct matrix transforming the vector <math>v</math> in the wanted orientation is just the transpose (<math>T^t</math>) of the one in the article. <br /> We have<br/> <math>S=R_z(\psi)R_y(\theta)R_x(\varphi) |
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</math><br /> and its elements are<br /> <math> |
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S = \begin{bmatrix} |
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c\psi c\theta & (c\psi s\theta s\varphi - s\psi c\varphi) & (c\psi s\theta c\varphi + s\psi s\varphi) \\ |
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s\psi c\theta & (s\psi s\theta s\varphi + c\psi c\varphi) & (s\psi s\theta c\varphi - c\psi s\varphi) \\ |
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-s\theta & c\theta s\varphi & c\theta c\varphi |
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\end{bmatrix}</math> |
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[[Special:Contributions/70.81.15.136|70.81.15.136]] ([[User talk:70.81.15.136|talk]]) 09:38, 10 June 2009 (UTC) |
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Well, I decided to clean the aerospace section, which is now (hopefully - I'm a bit sleepy) consistent. [[Special:Contributions/70.81.15.136|70.81.15.136]] ([[User talk:70.81.15.136|talk]]) 11:16, 10 June 2009 (UTC) |
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Non-clear Edits
WOAH! I have problems statements trying to relate to "principal rotations". it doesn't make any sense, and the wikipedia page that describes "principal axes" is wrong.
The first incorrect statement:
"It is important to notice that sometimes, informally, these names are used not to refer to the three angles, but to the rotations associated to each one of them[1], or even to rotations around the aircraft principal axes, creating confusion in terminology."
The second incorrect statement is in the caption:
"They can be seen as equivalent to principal rotations when the airplane principal axes and the reference axes are parallel"...
These are highly inaccurate statement. Roll/Pitch/Yaw are _ALWAYS_ used to describe the three angles, which are the consecutive rotations. They are not distinct from each other. The lateral/longitudinal axes are NOT Roll/Pitch axes, if there is such a thing. When the right wing is pointed downward, rotation about the longitudinal axis produces pure YAW. There is never any confusion in terminology. This statement needs to be removed.128.102.243.110 (talk) —Preceding undated comment added 03:33, 19 May 2009 (UTC).
The Juansempre edits are just incorrect, stating "It is important to notice that sometimes these names refer to the three Tait-Bryan angles[2], and sometimes to rotations around the aircraft principal axes[3][4][5], creating confusion in terminology." The references to the Glenn site are elementary school students worksheets, with simplifications so that children can understand basic concepts. There is no such confusion. 143.232.227.107 (talk) —Preceding undated comment added 08:35, 21 May 2009 (UTC).
- It cannot be hold at the same time that the confusion exists in learning material and that the confusion does not exist. Unfortunately, it does not only exist, but is quite common. Here is another link, this time a patent showing that the author uses the word yaw to refer to an intrinsic control [US Patent 6478262 - Flight control system for a hybrid aircraft in the yaw axis http://www.patentstorm.us/patents/6478262/claims.html]--213.170.46.90 (talk) 09:31, 25 May 2009 (UTC)
MAJOR REWORK
That was fast, whoever made those edits, I highly approve.76.102.19.74 (talk) 10:01, 26 November 2008 (UTC)
- I hope you don't mind, I modified the page to put the definition after the axis system definitions. 76.102.19.74 (talk) 10:08, 26 November 2008 (UTC)
Comments
Wow! This article is sketchy to say the least, filled with inaccurate statements that are just wrong, and really needs corrections and clean up. For anyone trying to learn about Euler angles and Tait-Bryan rotations, do not read this article. It is written by people just as confused as you are about the subject. The worst part is there are lots of websites that index/duplicate Wikipedia enteries automatically, so now when you search the web this article's text has been propagated.
- I suspect whoever wrote this article is a D student trying to get his head around Euler angles and Tait-Bryan rotations, specifically the paper "Development of a two-wheel contingency mode for the MAP spacecraft, Scott R. Starin and James R. O’Donnell, Jr.". If your professor is reading this article, I hope he fails you.
- Subsequent rotations to define one axis relative to another are always called Euler angles in every textbook I have used. If you want rotations about axes from an orthogonal basis, simply reverse the order, they are the same angles. If you want to think of the rotation angles as rotations about subsequently rotating axes, reverse the order again. They are still Euler angles. Since Euler angles do not specify exactly what order and exactly what axes to rotate about, I suspect that Tait-Bryan are the specific type of Euler angle that are used in aircraft (the standard roll/pitch/yaw).
- The statement "but not necessarily the principal axes of inertia" seems a useless and distracting side note, don't you think? Inertia and principle axes have really nothing to do with this.
- What the heck is the paper about the satellite doing at the end of this paper? There are millions of papers that are just as irrelevant we can add.
- "For a craft moving in the positive x direction, with the right side corresponding to the positive y direction, and the vertical underside corresponding to the positive z direction..." Very inaccurately stated. What axis system are you talking about, the relative wind axis? Why do we even care about moving axis system? Just stick with two axis systems, the world axis (like a NED system), and the body axis (like a x-fwd, y-right, z-down). Aircraft hardly ever move only in a positive x direction in these two axis system.
- The whole section about "Differences and similarities with Euler angles" needs to be thrown out. Everything it says is wrong. "You can visualize why this can be achieved with an example. An aeroplane doesn't need to perform a yaw to turn. It is enough to make a roll. Then the lift on the wings will force a pitch upwards." That is how you get a yaw angle! That is the definition! Rolling and pitching upwards gives you a yaw angle!
All I can say is, the entire text of this document should be deleted and destroyed.
76.102.19.74 (talk) 06:23, 26 November 2008 (UTC)
Woah, I am reading more of this article, each line is very hard to read because it is so inaccurate.
- "As in a moving frame all these things are true only for an instant, we can only assert them in the limit when time goes to zero. Thus, in a frame co-moving with the rotating system, Euler angles are equivalent to a special combination of Tait-Bryan angles in the limit when delta time goes to zero." ... Tait-Bryan angles are a specific instance of Euler angles is all that you need to say. It doesn't matter if you are in a "in a frame co-moving with the rotating system" or not. In fact, I am not quite sure what a "frame co-moving with the rotating system" means. I never saw a co-move before, except once when I was playing chess (i knocked over my knight while moving a pawn, I was penalized for a co-move).
- "The main usage is in a part of flight dynamics, called attitude control". Yes, no one else ever uses Euler angles, except for unmanned spacecraft. In which case they use reaction wheel. Not to mention momentum wheels, or gyroscopes, or manned spacecraft that use the same devices like the ISS.
- The section "Composition of intrinsical rotations" is just as bad. It starts with an incomplete sentence, and then gives a proof of... what?
- "calculus behind them is similar to the Frenet-Serret formulas". Too much to be said about that sentence.
I suggest the following... Delete everything but a few sentences from this entry, then correct those sentences. 76.102.19.74 (talk) 06:37, 26 November 2008 (UTC)
There's a link to Tait, but nothing about who Bryan is or was. That should be here. Michael Hardy 22:53, 1 Mar 2005 (UTC)
Are the rotations clockwise or counterclockwise? i.e. does it use the right-hand-rule or not? ~a 21:46, 17 October 2005 (UTC)
- By convention, all positive rotations are counter-clockwise as seen from the "end" of the respective axis towards the origin. That is, the right-hand-rule (or "right-hand-threaded-screw-rule") does apply. Sergey Khantsis 18:58, 12 November 2005 (UTC)
This was on the page:
Suggested change:
- In geometry, Tait-Bryan angles are three angles used to describe a general rotation in three-dimensional Euclidean space by three successive local rotations, once about the local x-axis, once about the new local y-axis, and once about the new local z-axis.
- Tait-Bryan differs from Euler angle rotations as Euler angles are applied to the fixed global coordinate system for each successive rotation.
Charles Matthews 10:35, 19 November 2005 (UTC)
- I can't be sure, but there is a George Bryan (mathematician) who corresponded briefly with Tait in 1901. Maybe that is the man. (No relation to the 18th century politician George Bryan) Urhixidur 22:23, 9 November 2006 (UTC)
I removed the examples of pitch and yaw. Both examples were of different concepts. The pitch example used angle-of-attack as an example of a pitch angle. The yaw angle example got mixed up and said that aircraft try to minimise their yaw angle to reduce drag (i.e., got mixed up with sideslip angle). If this were true, all aircraft would fly north. I also removed two See Alsos (Pitch Angle points to a physics article, and Roll Angle doesn't exist). Andy Ross 12:19, 22 February 2007 (UTC)
Added to first paragraph to point out these angles are a sub-set of the Euler angles (as shown in the paragraph dealing with their definition. Added a reference to the Wright-Patterson tech report WADC 58-17 which provides an excellent summary of the various methods of describing the orientation of one coordinate system with another i.e. 3 parameter: "Euler angles", 4 parameter: "Quarternions" ,9 parameter " direction cosines.
A great online reference dealing with all 3D rotations is http://ai.stanford.edu/~diebel/attitude/attitude.pdf. Won't take up editing this article yet, but it seems there are some inconsistencies. -FW
User:Plane Frames 9:24, 1 October 2008 (PDT)
Let's try to get the pictures right? The coordinate system shown for the plane is really a mixed-up mess. There are several orientations which are commonly used. However the key idea is this, follow the right hand rule, commonly using the thumb as the x-axis, fore-finger as the y-axis, and third finger as the z-axis. A positive rotation is always counterclockwise viewed down the postive side of the axis. So the figure has the following things wrong: assuming pitch/roll axis correct, then yaw axis is upside down and pitch rotation is backwards, assuming pitch/yaw axis correct, then roll axis is backwards and all 3 rotations are backwards, assuming roll/yaw axis correct, then pitch axis is backwards, and yaw rotation is backwards. Obviously there is some fixing that needs to be done here.
I am not happy with the composition of rotations, there are two fundamental rotations, rotation of the object in a fixed coordinate frame and rotation of the coordinate frame with respect to a fixed object. There is non-communitivity with respect to compositions of rotations, but the general rotation around an arbitrary axis in 3d coordinate systems is the general case, and it can be broken down into a composition of rotations about the x, y, and z axis, in a predefined order. You can specify the composition by matrix multiplication of each individual axis, either from the left hand side or right hand side depending upon the type of rotation (frame or object)
Sorry to generalize here, but the article needs more work.
-pi —Preceding unsigned comment added by Private individual (talk • contribs) 04:40, 2 October 2008 (UTC)
Error in rotation matrix
- It seems there were errors in the signs of various elements in the rotation matrix. I have stuck to the right-handed coordinate system with positive rotations being counterclockwise. V madhu (talk) 19:59, 7 April 2009 (UTC)
Error Confirmed
I can confirm the rotation matrix error. It seems to be related to which body coordinates are being used. For the 'standard' forward right down, which is claimed to be used here as the XYZ coordinates I obtain via Maple the 3x3 rotation matrix, [[cos(yaw)*cos(pitch), sin(yaw)*cos(pitch), -sin(pitch)], [cos(yaw)*sin(roll)*sin(pitch)-sin(yaw)*cos(roll), cos(yaw)*cos(roll)+sin(yaw)*sin(roll)*sin(pitch), sin(roll)*cos(pitch)], [sin(yaw)*sin(roll)+cos(yaw)*cos(roll)*sin(pitch), sin(yaw)*cos(roll)*sin(pitch)-cos(yaw)*sin(roll), cos(roll)*cos(pitch)]]
This matrix is the transpose of applying Rroll * Rpitch * Ryaw, since each of these rotations actually transforms from forward right down, to the fixed north east down (NED) . Also the figure ought to be made consistent with the forward right down body coordinates assumption. Here they make the z axis up instead of down.
Mattcbro (talk) 05:31, 6 June 2009 (UTC)
Corrections for consistency
I'm about to edit the article to expand it and correct a mistake I made, hence my overwriting of my previous text here. If you read the previous entry (and current corrections to the article I made yesterday), I assumed that the article wanted to show the coordinates of the object once rotated by the yaw, pitch, roll, a bit like the picture shows. But I think it wanted to show the transform matrix from a coordinate system to a rotated one fixed to the plane, like I was actually constructing (a basis change.) So everything is applied in reverse: obviously, the true basis change is wrong right now, since it shows just the rotation. But of course a basis change is just the inverse of the transform applied to vectors to orient them like the new frame (but still in original frame coordinate). IE I just need the RHS being inverted to truly expressed the basis change . As it is, it rotates vectors keeping them expressed in the fixed coordinate system xyz. Also, another thing that can get confusing for readers: sometimes on wiki, sometimes express just a rotation of vectors expressed in the same basis, but sometimes it expresses , the change of basis from the original basis to a rotated one. I will clarify this also. 70.81.15.136 (talk) 11:09, 11 June 2009 (UTC)
