Ellipse help

ColinCWare · ‎Dec 22, 2009

Hi faithful helpers,

I caused a real problem when I searched for help with this ellipse problem. Apparrently, the choice of words caused the search mechanism to balk and would not respond - PTC help came to handle the mechanism problem, not the ellipse problem.

As simple as it originally seemed, I have spent many hours and days on trying to find a way to plot an ellipse - and erect a "radius of curvature" on any selected position on the ellipse and point it inward or outward from the plotted elliptic paath.

I do not know what simple thing I am not performing that preents me from accomplishing the objective. Any suggestions? Or much wanted solutions?

Colin C eagle1@eaglmall.com

ColinCWare · ‎Dec 22, 2009

I unfortunately posted the former message accidently while making editing changes. so, the spelling is goofed also.

and please find the file here tat was to be put on the former message.

Colin C eagle1@eaglmall.com

ColinCWare · ‎Dec 22, 2009

OK this is as much my problem as is trying to plot a "radius of curvature" at any selected position on the ellipse.

SO, here I try the 3rd time a file you can download - the attached file.

Colin C eagle1@eaglmall.com

AlvaroDíaz · ‎Dec 23, 2009

Mathcad have not enough tools to work comfortable with cartesian implicit equations, like implicitplot or implicit derivative. Using parametric equations is more easy.

Regards. Alvaro.

ColinCWare · ‎Dec 23, 2009

Hi Alvaro,

This may be what I am missing. Please show me such parametric equations. This may be just what I need.

Colin C eagle1@eaglmall.com

AlvaroDíaz · ‎Dec 23, 2009

On 12/23/2009 12:20:34 PM, ColinCWare wrote:
>Please show me such parametric equations. This may be just what I need.

Do you download and read the attached file in the above post?

http://collab.mathsoft.com/~Mathcad2000/upload/Ellipse%20help(1).mcd

Regards. Alvaro.

ColinCWare · ‎Dec 23, 2009

Alvaro,

Your parametrics appears to be just what is needed. I would not know how todo this. Thank you.

How to save your file? Will Mcad 13 or Mcad 14 open it so I can put it to use? When I save it I cannot open it.

Regards, Colin C eagle1@eaglmall.com

AlvaroDíaz · ‎Dec 23, 2009

On 12/23/2009 4:59:26 PM, ColinCWare wrote:

>How to save your file? Will
>Mcad 13 or Mcad 14 open it so
>I can put it to use? When I
>save it I cannot open it.

No idea why happen this. If you can open the file, try to copy and paste into a new worksheet. Attached is the same in version 14.

Regards. Alvaro.

ptc-1368288 · ‎Dec 24, 2009

On 12/23/2009 6:19:40 PM, adiaz wrote:
>On 12/23/2009 4:59:26 PM, ColinCWare
>wrote:
>
>>How to save your file?
________________________

1. Click right on the attachment,
2. "Save as"
the "save as" is meant to save in your C:\Download
This folder is the one you should have created in the C:\ root. If you don't have it, create it. Then the first time you click right "save as", force Windows to save in YOUR C:\Download. Then in the future, anything you download will download in your default "Download" folder. Then back to an open Mathcad session, click on that downloaded attachment ... it will open.
That's as far as it can be doctored.

I have only one more question and maybe the last: why do you need the radius of curvature of an ellipse ? If the matter is the eventual swept area, maybe you should read Kepler and the associated "Elliptical integrals", and there is a Mathcad work sheet in the collab. I made it and will look if it can be found, if so will come back soon with the link.

jmG

ptc-1368288 · ‎Dec 24, 2009

... it does not seem to retrieve my work sheet ?

http://collab.mathsoft.com/read?119207,8
http://collab.mathsoft.com/read?123755,16

jmG

ptc-1368288 · ‎Dec 23, 2009

You may find interesting hints in Wiki.
So much work was done about ellipse 1d, 2d and posted. Ellipse is a quadric that solves simply and in the worst case, make it a circle of a, b radii.

jmG

ColinCWare · ‎Dec 23, 2009

Alvaro,

I cannot use the file.

jmG,

For you, easy; for me very, very difficult.

How can I download the file so I can use it. PTC has only very expensive requirements and some of the files that I need are no longer supported.

Colin C eagle1@eaglmall.com

ptc-1368288 · ‎Dec 23, 2009

On 12/23/2009 5:50:08 PM, ColinCWare wrote:
>Alvaro,
>
>I cannot use the file.
>
>jmG,
>
>For you, easy; for me very,
>very difficult.
>
>How can I download the file so
>I can use it. PTC has only
>very expensive requirements
>and some of the files that I
>need are no longer supported.
>
>Colin C eagle1@eaglmall.com
______________________________

Collin,

I'm actually Mathcadless all the ways.
I will try to read your problem next january.
You seem having several problems in a single sheet.

jmG

ptc-1368288 · ‎Dec 23, 2009

...

no help from wiki ?

http://en.wikipedia.org/wiki/Radius_of_curvature_(applications)

jmG

bbrady · ‎Dec 24, 2009

Does the attached help?
Regards,
Bill

ColinCWare · ‎Dec 24, 2009

To my very helpful Mcad collaborators,

Bill and jmG, I need the Radius (capitalized for recognition here) of curvature and its direction to determine the instantaneous centrifugal acceleration vector magnitude and direction. The files you have offered are helpful and Wiki; however, is missing vector information. Thanks to you both for your time and effort.

Alvaro, I have de-bugged my down loaded file of yours and it works beautifully. In fact my Mcad 6 Pro yields all the performance features your file provided, except,....

There is one unknown: What do the �stack(�)� functions in the plots do? Stacking is used for arrays. Your elements are single valued scalars, as near as I can tell. What other operations can be performed to yield the same results?

Happy Holidays!

Colin C eagle1@eaglmall.com

AlvaroDíaz · ‎Dec 24, 2009

On 12/24/2009 10:36:33 AM, ColinCWare wrote:

>There is one unknown: What do
>the �stack(�)� functions in
>the plots do?

I stack the center of the osculating circle with the point where this circle and the ellipse intercepts. For definition, at this point both curves (ellipse and circle) have the same tangent. With this two points you can draw a radious of the osculating circle. This radious also is in the normal line for both curves.

Also see the attached to draw polygons.

>Stacking is
>used for arrays. Your
>elements are single valued
>scalars, as near as I can
>tell.

Stacking scalars gives a columns vector.

>What other operations
>can be performed to yield the
>same results?

You can parametrize the line defined by the center of the circle and the curve point.

>Happy Holidays!

Thanks! The same to you.

Regards. Alvaro.

ColinCWare · ‎Dec 24, 2009

Thanks, Alvaro, for explaining the stack. My computer does not want to open or dowload your attachment. I don't think I will need it but it could be a great source of handling future problems I can get into.

Happy Holidays, Colin
Colin C eagle1@eaglmall.com

ColinCWare · ‎Dec 26, 2009

Alvaro,

your stack(...) refuses to stack by any modification I can make in Mcad 6 Pro.

Please describe what I must do to make the

y.c(t.o) operation not have to be an array when it stacked. ditto: x.c(t.o).

For others: simple; for me: very difficult.

Colin C eagle1@eaglmall.com

AlvaroDíaz · ‎Dec 26, 2009

On 12/26/2009 4:43:56 PM, ColinCWare wrote:
>Alvaro,
>
>your stack(...) refuses to
>stack by any modification I
>can make in Mcad 6 Pro.

Mathcad 6? That stack don't works with scalars is a minor issue comparing with the lot of problems that you can found implementing the proposed solution in this old version.

In mathcad 6 there are not Optimized option, so derivatives takes a lot of time to be numerically evaluated.

Also to plot a polygon (and the radious is one) you need to define a range variable for indexing the components.

Attached is developed in my mathcad 6 version and seems to work.

Regards. Alvaro.

ColinCWare · ‎Dec 27, 2009

Alvaro,

What you have done is perfect. It has all the features requested. And there is nothing slow in the calculations; results are instantaneous. I had not thought of using User Functions.

Thank you and Very Happy Holidays.

Colin C eagle1@eaglmall.com

ColinCWare · ‎Feb 27, 2010

I am reopening "Ellipse help" because this new problem is related to an ellipse definition.

The velocity of a body having mass orbiting in the gravity field of another mass, the radial distance between the masses is given and the vector of the velocity relative to the radius between the bodies is given.

A plane can be formed such that the velocity vector and the radius line are included in it. All motion is to remain in the 2-dimensional plane. �Looking down� on the plane, the motion of the orbiting body is counter-clockwise starting at 3 o�clock.

A circle could define the motion of the orbiting body. The next simplest circular path is an ellipse. Given the input data above, how can either path be determined?

And can the radius of curvature be found: 1) as the radius of the circle or 2) the semi-major and semi-minor axes of the ellipse relative to the given radial separation between the bodies to give radius of curvature equations for any position around the path?

Colin C eagle1@eaglmall.com

ptc-1368288 · ‎Jan 12, 2010

On 12/22/2009 10:05:49 PM, ColinCWare wrote:
...
>Any suggestions? Or much wanted solutions ?
>
>Colin C eagle1@eaglmall.com
_____________________________

"Or much wanted solutions"

In addition to the osculating circles,
here is the intersecting ellipse.
Watch some difficulty in initialising the solvers.

jmG