Timeline for Is a reasonable assumption to consider that the contact point of the Euler's Disk (with stationary center of mass) trace this finite bounded spiral?
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| May 5, 2022 at 20:36 | comment | added | Joako | Thanks. What I mean, thinking in a coin that is wobbling near this ending time, is that center of the coin is not moving in the XY plane, just falling in the Z axis, so instead of the flower-alike patter of your first graph it will look like more like an spiral. I would like to see How your result behave under similar conditions of the analysis I did? (I tried to do it by myself but I get lost with the used geometrical description) | |
| May 5, 2022 at 16:25 | comment | added | Eli | The second plot is the angle $~\beta~$ in degrees the x axis is the simulation time, the center of mass is the radius of the disk time cosine beta. What you mean by “the same vertical line” ? | |
| May 5, 2022 at 14:11 | comment | added | Joako | If you impose the restriction of keeping the center of mass in the same vertical line (as I am doing in the question).. How much are change your graphs under your model? (PS: the second one has missing the label on the vertical axis) | |
| Apr 23, 2022 at 21:54 | history | bounty ended | Joako | ||
| Apr 23, 2022 at 21:44 | comment | added | Eli | The theory is based on ODE second order differential equations that give you nonlinear equations like sin and cos terms . applied Taylor series you obtain the equations that I wrote | |
| Apr 23, 2022 at 17:37 | comment | added | Joako | Yes!.. I am meaning Partial differential equations.. I am getting lost if this nonlinear systems of diff. eq. of various variables are equivalent or not to PDEs, since by one side, their derivatives only depends on time (not PDE), but terms like $\ddot{\varphi}/\dot{\beta} \cong \frac{d}{d\beta}\dot{\varphi}$ so now there could be transform on derivatives in multilple variables.. so I don't know if a nonlinear system of diff eqs of multiple variables is equivalent or not to a PDE | |
| Apr 23, 2022 at 6:46 | comment | added | Eli | The only nonlinear state is $\beta$ all others are linearized . I can write you the complete nonlinear equations. Notice that in my equations there is no friction force involved. What is PDE partial differential equations ? Also the simulations results are done with the complete nonlinear equations. | |
| Apr 23, 2022 at 6:16 | comment | added | Joako | a question: the system of nonlinear differential eqs. between brackets, Is conceptually different from a PDE, right?... or it can be converted into an PDE by some manipulations? | |
| Apr 22, 2022 at 20:32 | comment | added | Joako | Thanks for answering @Eli. I saw the paper and is a bit more complicated that the one a cited on the question. They takes less assumptions as I, like keeping the center of mass of the disk in the same vertical point, reason why the plots shows that "petals-like" turns. I found really interesting that in some of their dissipation terms they consider terms that includes the function $\text{sgn}(\cdot)$, which also appear in the non-Lipschitz terms of the paper by V.T. Haimo: $\dot{x}=-\text{sgn}(x)\sqrt{|x|},\,x(0)=1$ as example admits the solution $x(t)=\frac{1}{4}(1-t/2+|1-t/2|)^2$. | |
| Apr 22, 2022 at 16:40 | history | undeleted | Eli | ||
| Apr 22, 2022 at 16:40 | history | edited | Eli | CC BY-SA 4.0 |
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| Apr 22, 2022 at 16:37 | history | deleted | Eli | via Vote | |
| Apr 22, 2022 at 16:31 | history | undeleted | Eli | ||
| Apr 22, 2022 at 16:30 | history | edited | Eli | CC BY-SA 4.0 |
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| Apr 22, 2022 at 16:01 | history | deleted | Eli | via Vote | |
| Apr 22, 2022 at 16:01 | history | edited | Eli | CC BY-SA 4.0 |
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| Apr 22, 2022 at 15:55 | history | answered | Eli | CC BY-SA 4.0 |