topic Re: Help to solve a non-linear ODE in mathCAD 15 in PTC Mathcad
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/642975#M188462
<P>Hi,</P>
<P> </P>
<P>when i tried to put the relevant units in (ant altered the values accordingly) it didn't want to work - various warnings (see attached). Any pointers?</P>Mon, 06 Jan 2020 12:54:22 GMTPyros11112020-01-06T12:54:22ZHelp to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/641767#M188345
<P>Hi,</P>
<P> </P>
<P>I am attempting to dynamically model the behaviour of granular solids in a rotary kiln using known equations, however i am having trouble setting up the following ODEs in mathCAD for the model....can anyone help. I have included the key points i am trying to model in Mathcad.</P>
<P> </P>
<DIV id="tinyMceEditorPyros1111_2" class="mceNonEditable lia-copypaste-placeholder"> </DIV>
<P> </P>
<P><span class="lia-inline-image-display-wrapper lia-image-align-inline" image-alt="bed height equation.PNG" style="width: 535px;"><img src="https://community.ptc.com/t5/image/serverpage/image-id/22148iDAF4AA36EC95A221/image-size/large?v=v2&px=999" role="button" title="bed height equation.PNG" alt="bed height equation.PNG" /></span></P>
<P>boundary condition: <span class="lia-inline-image-display-wrapper lia-image-align-inline" image-alt="boundary condition.PNG" style="width: 165px;"><img src="https://community.ptc.com/t5/image/serverpage/image-id/22149iB98E6E9B424472DD/image-size/large?v=v2&px=999" role="button" title="boundary condition.PNG" alt="boundary condition.PNG" /></span></P>
<P>where h0 is a fixed value (say 10% of the value of R).</P>
<P> </P>
<P>From the above i'm looking to be able to determine the bed height (h) at any axial location (z) along the kiln tube.</P>
<P> </P>
<P>Subsequently equations for Cross section area of the granular bed and residence time of the granular transport through the kiln (as a function of bed depth (h)) follow on from this...</P>
<P> </P>
<P>Cross section area:</P>
<P> </P>
<P><span class="lia-inline-image-display-wrapper lia-image-align-inline" image-alt="Cross section Area equation.PNG" style="width: 475px;"><img src="https://community.ptc.com/t5/image/serverpage/image-id/22151iB64FD337D0BD4012/image-size/large?v=v2&px=999" role="button" title="Cross section Area equation.PNG" alt="Cross section Area equation.PNG" /></span></P>
<P>Residence time</P>
<P><span class="lia-inline-image-display-wrapper lia-image-align-inline" image-alt="residence time equation.PNG" style="width: 297px;"><img src="https://community.ptc.com/t5/image/serverpage/image-id/22152i17EA0A59B19F5BCE/image-size/large?v=v2&px=999" role="button" title="residence time equation.PNG" alt="residence time equation.PNG" /></span></P>
<P>So essentially i am looking to use MatCAD to find the residence time (t), given fixed values for: n (rotation speed in rpm), R (radius of kiln in m), D (diameter of kiln in m), angle of repose of the material (beta), angle of inclination of the kiln (theta), mass flow rate <FONT size="3">(m<FONT size="1">s</FONT>)</FONT> , bulk density of material (rho), axial length of the kiln tube (z).</P>
<P> </P>
<P>My initial attempt using ODEsolver block did not get that far and with limited success (see attached) and seems very temperamental depending on what values are used and cannot utilise units for the variables (hence why they are all unitless.</P>
<P> </P>
<DIV id="tinyMceEditorPyros1111_0" class="mceNonEditable lia-copypaste-placeholder"> </DIV>
<P> </P>Fri, 20 Dec 2019 11:25:57 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/641767#M188345Pyros11112019-12-20T11:25:57ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/641780#M188346
<P>Hi,</P>
<P><span class="lia-inline-image-display-wrapper lia-image-align-inline" image-alt="1111.jpg" style="width: 736px;"><img src="https://community.ptc.com/t5/image/serverpage/image-id/22155iAF717D9B4E9F6336/image-size/large?v=v2&px=999" role="button" title="1111.jpg" alt="1111.jpg" /></span></P>Fri, 20 Dec 2019 13:53:17 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/641780#M188346-MFra-2019-12-20T13:53:17ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/641957#M188353
<P>Thanks very much !!</P>Mon, 23 Dec 2019 08:06:03 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/641957#M188353Pyros11112019-12-23T08:06:03ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/641958#M188354
<P>is there anyway to do it using the specific units for the different variables?</P>Mon, 23 Dec 2019 08:09:25 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/641958#M188354Pyros11112019-12-23T08:09:25ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/641959#M188355
<P>thanks. - will this work using specific units with the variables?</P>Mon, 23 Dec 2019 08:10:56 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/641959#M188355Pyros11112019-12-23T08:10:56ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/641960#M188356
<P>In Mathcad 15 and before you cannot have units with an Odesolve (unless they cancel out).</P>
<P>One of the advantages of Prime is that you can.</P>
<P> </P>
<P>Success!<BR />Luc</P>Mon, 23 Dec 2019 08:25:47 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/641960#M188356LucMeekes2019-12-23T08:25:47ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/641962#M188357
<P>sorry to be a bother again but when i try and put this in it still doesn't seem to work properly for the last bit - says variable undefined??? any pointers on what im doing wrong?</P>
<P> </P>
<P><span class="lia-inline-image-display-wrapper lia-image-align-inline" image-alt="Capture.PNG" style="width: 978px;"><img src="https://community.ptc.com/t5/image/serverpage/image-id/22198iDF005E53C9202F32/image-size/large?v=v2&px=999" role="button" title="Capture.PNG" alt="Capture.PNG" /></span></P>Mon, 23 Dec 2019 08:40:28 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/641962#M188357Pyros11112019-12-23T08:40:28ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/641965#M188358
<P>my fault - was using a Boolean equals sign.</P>Mon, 23 Dec 2019 08:58:27 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/641965#M188358Pyros11112019-12-23T08:58:27ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/641977#M188359
<P>If constants and variables are dimensioned, they must be rendered dimensionless before the Odesolve block. After it, you can redimension them again.</P>Mon, 23 Dec 2019 10:19:32 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/641977#M188359-MFra-2019-12-23T10:19:32ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/642001#M188360
<P>tried putting the same thing into Mathcad prime (so i could use units as suggested) but i just get various errors... clearly its done a bit differently in prime and i am missing something - any help?</P>Mon, 23 Dec 2019 11:55:03 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/642001#M188360Pyros11112019-12-23T11:55:03ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/642002#M188361
<P><SPAN style="display: inline !important; float: none; background-color: #ffffff; color: #3d3d3d; font-family: 'Tex Gyre Adventor','Lato','Helvetica Neue',Helvetica,Arial,sans-serif; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 300; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;">tried putting the same thing into Mathcad prime (so i could use units as suggested) but i just get various errors... clearly its done a bit differently in prime and i am missing something - any help?</SPAN></P>Mon, 23 Dec 2019 11:58:03 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/642002#M188361Pyros11112019-12-23T11:58:03ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/642020#M188362
<P>Prime is different than 15.</P>
<P> </P>
<P>Did you translate the 15 file, or start a new file?</P>
<P> </P>
<P>Can you post your Prime sheet? (Usually gets prompter and more focused help.</P>Mon, 23 Dec 2019 12:51:09 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/642020#M188362Fred_Kohlhepp2019-12-23T12:51:09ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/642041#M188364
<P>tried to start a new one... see attached.</P>Mon, 23 Dec 2019 13:17:42 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/642041#M188364Pyros11112019-12-23T13:17:42ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/642063#M188365
<P>You don't need guess values for an odesolve. Put all variable definitions above, out of the guess part of the solve block.</P>
<P> </P>
<P>Success!<BR />Luc</P>Mon, 23 Dec 2019 16:10:05 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/642063#M188365LucMeekes2019-12-23T16:10:05ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/642090#M188366
<P>Concerning the odesolve block it should make no difference if you define your constants inside the solve block or above. But if you define them inside, the values are not available below and outside of the solve block. So it may be a good idea anyway to define those constants above the block.</P>
<P>The reason for your solve block failing is the value of your variable R.w.</P>
<P>Compared to your Mathcad sheet you used different values for m.s and R.w in your Prime attempt.</P>
<P>Especially the low value 0.25 for R.w compared to the value 2 you had in Mathcad seems to make the solve block fail. It looks like (with the other values unchanged) R.w must be at least 0.502 or larger.</P>
<P><span class="lia-inline-image-display-wrapper lia-image-align-inline" image-alt="Werner_E_0-1577134407264.png" style="width: 400px;"><img src="https://community.ptc.com/t5/image/serverpage/image-id/22246i4C1355BE84CE8933/image-size/medium?v=v2&px=400" role="button" title="Werner_E_0-1577134407264.png" alt="Werner_E_0-1577134407264.png" /></span></P>
<P> </P>Mon, 23 Dec 2019 21:01:04 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/642090#M188366Werner_E2019-12-23T21:01:04ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/642152#M188370
<P>One other thing:</P>
<P>Theta and beta are angles I guess. You provided a large value for Theta that you did not intend: 40, that is 40 radians, not degrees!</P>
<P>Sad to say that when I change to 40 degrees and 3 degrees respectively, no solution is found...</P>
<P>Success!</P>
<P>Luc</P>Tue, 24 Dec 2019 16:27:39 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/642152#M188370LucMeekes2019-12-24T16:27:39ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/642975#M188462
<P>Hi,</P>
<P> </P>
<P>when i tried to put the relevant units in (ant altered the values accordingly) it didn't want to work - various warnings (see attached). Any pointers?</P>Mon, 06 Jan 2020 12:54:22 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/642975#M188462Pyros11112020-01-06T12:54:22ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/642983#M188463
<P>hi again,</P>
<P> </P>
<P>thanks again for your previous reply - i have been looking over it and trying to use the more accurate values to see what comes out and noticed i had initially described the inmitial condition for the ODEsolver as Hx(0)=0.01, whereas what i wanted to do was define it as Hx(L) = 0.01. However, when i do this in the Mathcad (See attached) it doesn't work and says the endpoints cannot be the same in the solve block?</P>
<P><span class="lia-inline-image-display-wrapper lia-image-align-inline" image-alt="Capture 4.PNG" style="width: 423px;"><img src="https://community.ptc.com/t5/image/serverpage/image-id/22418i26E4B800D494BCEC/image-dimensions/423x221?v=v2" width="423" height="221" role="button" title="Capture 4.PNG" alt="Capture 4.PNG" /></span></P>
<P>can you explain why and how to make it work for this end constraint please?</P>Mon, 06 Jan 2020 13:36:56 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/642983#M188463Pyros11112020-01-06T13:36:56ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643019#M188464
<OL>
<LI>The initial conditions must be given with the appropriate units. Its not necessary to write 0m instead of just 0, but its good habit to do so, too</LI>
<LI>The solve block fails if R is lower than 1.97 m. You'll have to check your equation or the other values assigned if you think that R=0,5m should yield a valid result. I notice that you changed several values compared to the file I posted (where R must had a value of at least 0.502).</LI>
<LI>To plot with units on the abscissa you need to define a range variable. I have chosen z.plot as the name for this variable which is only to be used for plotting, but you can chose any name you like (even simply z :-).</LI>
</OL>
<P><span class="lia-inline-image-display-wrapper lia-image-align-inline" image-alt="Werner_E_0-1578322799185.png" style="width: 400px;"><img src="https://community.ptc.com/t5/image/serverpage/image-id/22433iC8F166208013BF53/image-size/medium?v=v2&px=400" role="button" title="Werner_E_0-1578322799185.png" alt="Werner_E_0-1578322799185.png" /></span></P>
<P> </P>Mon, 06 Jan 2020 15:00:39 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643019#M188464Werner_E2020-01-06T15:00:39ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643021#M188465
<P>Hi,</P>
<P> </P>
<P>thanks for this - i see how that works now.</P>
<P> </P>
<P>I was also trying to alter the initial condition for Hz as its not correct and should be Hz(L)=0.01 rather than Hz(0)=0.01 however this doesn't seem to work? does something else need to be changed?</P>Mon, 06 Jan 2020 15:04:57 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643021#M188465Pyros11112020-01-06T15:04:57ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643024#M188466
<P>Try integrating in reverse from Lretort to zero:</P>
<P> </P>
<P><span class="lia-inline-image-display-wrapper lia-image-align-inline" image-alt="reverse.JPG" style="width: 428px;"><img src="https://community.ptc.com/t5/image/serverpage/image-id/22434i34BE4CB0F0D262A5/image-size/large?v=v2&px=999" role="button" title="reverse.JPG" alt="reverse.JPG" /></span> </P>
<P>See attached.</P>
<P>Alan</P>
<P> </P>Mon, 06 Jan 2020 15:17:00 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643024#M188466AlanStevens2020-01-06T15:17:00ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643064#M188467
<P>Units in ODE's in Mathcad 15 pose a significant challenge: take them out incorrectly and the problem is not properly scaled. One solution I found was to use the function "UnitsOf". </P>
<P>If you define a variable with a unit (L := 2 ft), to use it in an ODE it must have the units stripped. Clearly, dividing by inches, feet, or meters will create different values. Mathcad has a consistent unit system (when I type L = my version 15 would have defaulted to meters,) to get all the scaling correct, divide each expression by the function. So L becomes "L/UnitsOf(ft)". Note that "L/UnitsOf(L) would work as well EXCEPT if you have a unit mismatch the first expression would catch it, the second one would not. (If L had dimensions of velocity the first expression (UnitsOf(ft) would crash, the second would happily just strip the wrong units.</P>
<P> </P>
<P>But ODE's in Prime can use units. . .</P>Mon, 06 Jan 2020 18:52:17 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643064#M188467Fred_Kohlhepp2020-01-06T18:52:17ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643073#M188468
<BLOCKQUOTE><HR /><LI-USER uid="309715"></LI-USER> wrote:<BR />
<P>Hi,</P>
<P> </P>
<P>thanks for this - i see how that works now.</P>
<P> </P>
<P>I was also trying to alter the initial condition for Hz as its not correct and should be Hz(L)=0.01 rather than Hz(0)=0.01 however this doesn't seem to work? does something else need to be changed?</P>
<HR /></BLOCKQUOTE>
<P>Alan already solved that. Its as simple as writing the desired inital condition in the solve block and set the "end" value to zero. No R can be a higher value, too.</P>
<P><span class="lia-inline-image-display-wrapper lia-image-align-inline" image-alt="Werner_E_0-1578342963850.png" style="width: 400px;"><img src="https://community.ptc.com/t5/image/serverpage/image-id/22441i5AB6358CBA9742E2/image-size/medium?v=v2&px=400" role="button" title="Werner_E_0-1578342963850.png" alt="Werner_E_0-1578342963850.png" /></span></P>
<P> </P>Mon, 06 Jan 2020 20:37:42 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643073#M188468Werner_E2020-01-06T20:37:42ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643132#M188470
<P>Hmmm interesting... trying your example out for myself i get this:</P>
<P> </P>
<P><span class="lia-inline-image-display-wrapper lia-image-align-inline" image-alt="Capture x.PNG" style="width: 152px;"><img src="https://community.ptc.com/t5/image/serverpage/image-id/22451iA4E09CFFB765E20D/image-size/large?v=v2&px=999" role="button" title="Capture x.PNG" alt="Capture x.PNG" /></span></P>
<P>is this correct? it still looks like it has defaulted to metres i.e 2ft = 0.61m?</P>Tue, 07 Jan 2020 08:51:04 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643132#M188470Pyros11112020-01-07T08:51:04ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643137#M188471
<P>applying what your units workaround to my current Mathcad 15 sheet i cant get it to run - see attached? what have i missed?</P>Tue, 07 Jan 2020 09:16:53 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643137#M188471Pyros11112020-01-07T09:16:53ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643178#M188473
<P><SPAN>is this correct? it still looks like it has defaulted to metres i.e 2ft = 0.61m?</SPAN></P>
<P> </P>
<P><SPAN>You are correct-- 2 ft has become 0.61, but there are no attached units. So your equation (ODE) will be rendered unitless but with proper scaling.</SPAN></P>
<DIV id="tinyMceEditorFredKohlhepp_1" class="mceNonEditable lia-copypaste-placeholder"> </DIV>Tue, 07 Jan 2020 13:10:49 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643178#M188473Fred_Kohlhepp2020-01-07T13:10:49ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643252#M188474
<P>The unitless values are dependent on the unit system chosen.</P>
<P>With unit system "U.S."you get:</P>
<P><span class="lia-inline-image-display-wrapper lia-image-align-inline" image-alt="LucMeekes_0-1578431431077.png" style="width: 400px;"><img src="https://community.ptc.com/t5/image/serverpage/image-id/22473i5ABE69CC5C37A2ED/image-size/medium?v=v2&px=400" role="button" title="LucMeekes_0-1578431431077.png" alt="LucMeekes_0-1578431431077.png" /></span></P>
<P>But with unit system set to "S.I." you get:</P>
<P><span class="lia-inline-image-display-wrapper lia-image-align-inline" image-alt="LucMeekes_1-1578431514978.png" style="width: 400px;"><img src="https://community.ptc.com/t5/image/serverpage/image-id/22474i71CDF2DF18C90F00/image-size/medium?v=v2&px=400" role="button" title="LucMeekes_1-1578431514978.png" alt="LucMeekes_1-1578431514978.png" /></span></P>
<P>Success!<BR />Luc</P>Tue, 07 Jan 2020 21:12:25 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643252#M188474LucMeekes2020-01-07T21:12:25ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643254#M188475
<P>Thanks Luc!</P>
<P> </P>
<P>The point I was trying to make is that to solve an ODE correctly it must be properly scaled; using the UnitsOf function ensures that Mathcad will scale the equation correctly into whichever default system is selected. The solution can then be "reunitized" by multiplying by UnitsOf(the correct type of dimension).</P>Tue, 07 Jan 2020 21:22:05 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643254#M188475Fred_Kohlhepp2020-01-07T21:22:05ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643261#M188476
<P>There are a couple things I've noticed, tried hard to address; see comments pdf attached</P>Tue, 07 Jan 2020 21:51:15 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643261#M188476Fred_Kohlhepp2020-01-07T21:51:15ZRe: Help to solve a non-linear ODE in mathCAD 15
https://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643269#M188477
<P>Your rotational speed may be a litle low. 1/3 of a rotation per minute apparently isn't enough, 333 rotations per minute does give a solution.</P>
<P>Mind that you don't have to use the UnitsOf function to cancel units, and 'rad' is a unitless 'unit' anyway. You can also divide the units out directly.</P>
<P>See below.</P>
<P><span class="lia-inline-image-display-wrapper lia-image-align-inline" image-alt="LM_20200107_Odesolve1.png" style="width: 663px;"><img src="https://community.ptc.com/t5/image/serverpage/image-id/22477i52069D8A7574DAB4/image-size/large?v=v2&px=999" role="button" title="LM_20200107_Odesolve1.png" alt="LM_20200107_Odesolve1.png" /></span></P>
<P>Then, with Dw reduced to 0.5 m,and the minus sign in front of the derivative removed, I get:</P>
<P><span class="lia-inline-image-display-wrapper lia-image-align-inline" image-alt="LM_20200107_Odesolve2.png" style="width: 656px;"><img src="https://community.ptc.com/t5/image/serverpage/image-id/22478iDC4A9DB3F75A1EF5/image-size/large?v=v2&px=999" role="button" title="LM_20200107_Odesolve2.png" alt="LM_20200107_Odesolve2.png" /></span></P>
<P>Success!<BR />Luc</P>Tue, 07 Jan 2020 22:33:09 GMThttps://community.ptc.com/t5/PTC-Mathcad/Help-to-solve-a-non-linear-ODE-in-mathCAD-15/m-p/643269#M188477LucMeekes2020-01-07T22:33:09Z