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Intrinsic coordinates
What are they? My mechanics questions keeps saying to use them but they don't seem to be that well known and I can't find anything about them in the textbooks. Do they have an alternate name or something?
They are simply a different way to define the position of a point in space.
You can use cartesian, polar, or you can use intrinsic.
Basically, imagine there's a point P which lies on a fuction y = f(x).
Now, the coordinates of that point in cartesian coordinates is simply (x,y). In polar coordinates, the point is .
In intrinsic coordinates you use two different coordinates to define a point P, and these coordinates are . s is the length of the "arc" from a fixed point in space, A (usually the origin of the x-y coordinate system), to P, and is the angle that the tangent to the curve y=f(x) makes with the positive x axis at point P.
It's called intrinsic because the coordinates make reference to the curve itself, rather than making reference to a separate coordinate system which describes the whole space. Intrinsic coordinates make no reference to points that are not on the curve, whereas polar and cartesian define a space, and then we narrow that space down to points that exist on the curve. (Although is still KIND of makes reference to the cartesian system since is defined with respect to the x axis and is usually defined with respect to the origin.
There is some info about it here:
http://books.google.co.uk/books?id=gNItsN82vXkC&pg=RA2-PA361&lpg=RA2-PA361&dq=intrinsic+coordinates+mathematics&source=bl&ots=hPNRU_LcZ_&sig=DSdloc5984jau7DoJK8psBrnJdM&hl=en&ei=unCRS_vOIs-TjAe--aX3Cw&sa=X&oi=book_result&ct=result&resnum=6&ved=0CBoQ6AEwBQ#v=onepage&q=&f=false
I have personally never used intrinsic coordinates for any practical purpose and don't ever intend to. They are pointless, since they are based on a system that is much simpler to use, and they are extremely limited for use.
You can use cartesian, polar, or you can use intrinsic.
Basically, imagine there's a point P which lies on a fuction y = f(x).
Now, the coordinates of that point in cartesian coordinates is simply (x,y). In polar coordinates, the point is .
In intrinsic coordinates you use two different coordinates to define a point P, and these coordinates are . s is the length of the "arc" from a fixed point in space, A (usually the origin of the x-y coordinate system), to P, and is the angle that the tangent to the curve y=f(x) makes with the positive x axis at point P.
It's called intrinsic because the coordinates make reference to the curve itself, rather than making reference to a separate coordinate system which describes the whole space. Intrinsic coordinates make no reference to points that are not on the curve, whereas polar and cartesian define a space, and then we narrow that space down to points that exist on the curve. (Although is still KIND of makes reference to the cartesian system since is defined with respect to the x axis and is usually defined with respect to the origin.
There is some info about it here:
http://books.google.co.uk/books?id=gNItsN82vXkC&pg=RA2-PA361&lpg=RA2-PA361&dq=intrinsic+coordinates+mathematics&source=bl&ots=hPNRU_LcZ_&sig=DSdloc5984jau7DoJK8psBrnJdM&hl=en&ei=unCRS_vOIs-TjAe--aX3Cw&sa=X&oi=book_result&ct=result&resnum=6&ved=0CBoQ6AEwBQ#v=onepage&q=&f=false
I have personally never used intrinsic coordinates for any practical purpose and don't ever intend to. They are pointless, since they are based on a system that is much simpler to use, and they are extremely limited for use.
So when these Mechanics questions ask me to use intrinsic coordinates, could I (if the question permitted it) just as easily use Cartesians or polars?
gangsta316
So when these Mechanics questions ask me to use intrinsic coordinates, could I (if the question permitted it) just as easily use Cartesians or polars?
I should think so.
Motion is either rectilinear or circular or a mix of both in the most common applications on Engineering. I really can't imagine a situation where it would be easier to use intrinsic coordinates than polar or rectilinear.
I've been a student of Aeronautical Engineering for 3 years now and have never once used a coordinate system that wasn't rectilinear, polar, spherical or cylindrical.
Helvete
I should think so.
Motion is either rectilinear or circular or a mix of both in the most common applications on Engineering. I really can't imagine a situation where it would be easier to use intrinsic coordinates than polar or rectilinear.
I've been a student of Aeronautical Engineering for 3 years now and have never once used a coordinate system that wasn't rectilinear, polar, spherical or cylindrical.
Motion is either rectilinear or circular or a mix of both in the most common applications on Engineering. I really can't imagine a situation where it would be easier to use intrinsic coordinates than polar or rectilinear.
I've been a student of Aeronautical Engineering for 3 years now and have never once used a coordinate system that wasn't rectilinear, polar, spherical or cylindrical.
Here's an example of a question that was given and solved using intrinsic coordinates.
A smooth wire in the shape of the parabola y = x^2 stands with its positive y-axis directed vertically upwards. A bead of mass m slides on the wire and is released from rest at height y = 4. When the bead is at height y = 2 find the tangential and normal components of acceleration, and show that the reaction R on the wire is 17mg/27.
Could this be done easily using polars or another coordinate system?
Edexcel Mechanics M6 2000 specification from Amazon.
MadAsMaths has two booklets on this.
MadAsMaths has two booklets on this.
(edited 5 years ago)
Original post by 111Daniel111
Edexcel Mechanics M6 2000 specification from Amazon.
MadAsMaths has two booklets on this.
MadAsMaths has two booklets on this.
Not a lot of point replying to an 8 year old thread...
Original post by DFranklin
Not a lot of point replying to an 8 year old thread...
This topic has been off the A level/physics syllabus for over 10 years and is not used a great deal even at degree level and only people who really enjoy mathematics are likely to be doing intrinsic coordinates, so I have responded for any student who asks the student room for help.
Original post by 111Daniel111
This topic has been off the A level/physics syllabus for over 10 years and is not used a great deal even at degree level and only people who really enjoy mathematics are likely to be doing intrinsic coordinates, so I have responded for any student who asks the student room for help.
If you think someone who asked a question 8 years ago is going to be helped by your response, I think you are a little overoptimistic.
Bumping old threads is frowned upon here.
Original post by DFranklin
If you think someone who asked a question 8 years ago is going to be helped by your response, I think you are a little overoptimistic.
Bumping old threads is frowned upon here.
Bumping old threads is frowned upon here.
I said 'anyone' and it is possible that someone will ask a question about the topic and come onto this thread. I know that it is unlikely that the person who asked the original question needs an answer now.
Also, why is it frowned upon to respond to old threads? Seems like a silly thing to frown upon.
Original post by 111Daniel111
I said 'anyone' and it is possible that someone will ask a question about the topic and come onto this thread. I know that it is unlikely that the person who asked the original question needs an answer now.
Also, why is it frowned upon to respond to old threads? Seems like a silly thing to frown upon.
Also, why is it frowned upon to respond to old threads? Seems like a silly thing to frown upon.
In particular, it's really common for a 20+ post thread to get bumped to the top, people start responding to the original post (often not realising that it's 8 years old), and a lot of people's time is wasted.
Regardless of what you think, there's a specific TSR-wide option for reporting a post that bumps an old thread - it's not just me (or particular foibles of the Maths sub-forum) being difficult here.
Original post by DFranklin
Because the order things are presented is "most recently posted in". So when you respond to an old thread, people see it move to the top and think that something new has happened.
In particular, it's really common for a 20+ post thread to get bumped to the top, people start responding to the original post (often not realising that it's 8 years old), and a lot of people's time is wasted.
Regardless of what you think, there's a specific TSR-wide option for reporting a post that bumps an old thread - it's not just me (or particular foibles of the Maths sub-forum) being difficult here.
In particular, it's really common for a 20+ post thread to get bumped to the top, people start responding to the original post (often not realising that it's 8 years old), and a lot of people's time is wasted.
Regardless of what you think, there's a specific TSR-wide option for reporting a post that bumps an old thread - it's not just me (or particular foibles of the Maths sub-forum) being difficult here.
I am not wasting other people's time. When someone clicks on a thread they can see the time stamp, right? So when they respond their time may be wasted but this is not the fault of the person who responded. Is it not possible to make threads which are older than say, 5 years old, impossible to reply to (i.e. archive them)?
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