Error

 4 Pages<1234>
 Previous Topic Next Topic
 Razonar #41 Posted : 08 November 2018 23:37:16(UTC) Rank: Advanced MemberGroups: Registered Joined: 28/08/2014(UTC)Posts: 445Was thanked: 254 time(s) in 155 post(s) Originally Posted by: Ber7 The parameterization by Draghilev method.The starting point is taken near the bifurcation point (0,0).Just a very little modifications: using norme(J) and the SMath ability for handling undefined parameters. ContourTifoleum.sm (17kb) downloaded 21 time(s).Best regards.Alvaro. 2 users thanked Razonar for this useful post. on 09/11/2018(UTC),  on 09/11/2018(UTC)
 Ber7 #42 Posted : 09 November 2018 11:29:40(UTC) Rank: Advanced MemberGroups: Registered Joined: 15/07/2010(UTC)Posts: 330Location: Beer-ShevaWas thanked: 425 time(s) in 230 post(s) Thank you, Alvaro. The norme function simplifies the code and reduces the calculation time.Example of using norme when solving ODE LorenzPointsAreEquidistantc.sm (7kb) downloaded 24 time(s). 2 users thanked Ber7 for this useful post. on 09/11/2018(UTC),  on 09/11/2018(UTC)
 Razonar #43 Posted : 09 November 2018 19:08:46(UTC) Rank: Advanced MemberGroups: Registered Joined: 28/08/2014(UTC)Posts: 445Was thanked: 254 time(s) in 155 post(s) Hi Ber. I don't remember to read nothing in the literature about equally spaced points in the numerical solution of the ode, except for the opposite: adaptive steps, but referring for the time variable, not the X,Y,Z solution points. About how you apparently get the same distance between solution points, i.e. sqrt(X^2+Y^2+Z^2), I guess that the background theory must to be in the Draghilev method and how the solution (X,Y,Z) is obtained from the differential equation. You have a very interesting point for investigate and publish about it.I try to investigate the relationship between the symbolic ode solution and the paramatrization, but the symbolic solutions are quite complicated, and I don't have simple examples.Apparently the distance between the points is 1 (guess can be easily proved because you divide by the norme the system), and this seems to provide more stable numerical solutions for the system (can be applied here Lyapunov's theorems?)Unfortunately in this example I introduce the factor 1/1000 for avoid numerical over max limit error for the case without norme.Best regards.Alvaro.
 Jean Giraud #44 Posted : 11 November 2018 05:39:23(UTC) Rank: Advanced MemberGroups: Registered Joined: 04/07/2015(UTC)Posts: 4,307Was thanked: 751 time(s) in 592 post(s) Originally Posted by: Ber7 The parameterization by Draghilev method.The starting point is taken near the bifurcation point (0,0).Thanks Ber7, gorgeous For this particular Trifolium, once created it is easy to collectas many as desired to any scale corresponding to Draghilev 'a'The great tool here, is the bidirectional fmesh(f(x),x0,x1,mesh)Cheers ... Jean 2D Parametric Plot [Create Trifolium].sm (32kb) downloaded 21 time(s).
 Ber7 #45 Posted : 11 November 2018 08:48:41(UTC) Rank: Advanced MemberGroups: Registered Joined: 15/07/2010(UTC)Posts: 330Location: Beer-ShevaWas thanked: 425 time(s) in 230 post(s) Thank you Jean, I suggest a small change in the animation. TrifoliumAnim.sm (25kb) downloaded 19 time(s).Edited by user 11 November 2018 12:44:29(UTC)  | Reason: Not specified
 Jean Giraud #46 Posted : 11 November 2018 17:48:44(UTC) Rank: Advanced MemberGroups: Registered Joined: 04/07/2015(UTC)Posts: 4,307Was thanked: 751 time(s) in 592 post(s) Originally Posted by: Ber7 I suggest a small change in the animation.Thanks Ber7 ... even more compacted.Trifolium:=stack(b1,b2,b3,b4) from inversing f4(x) <= f3(x). 0Anim Trifolium [Windmill Ber7].sm (26kb) downloaded 19 time(s).
 Ber7 #47 Posted : 24 November 2018 22:03:02(UTC) Rank: Advanced MemberGroups: Registered Joined: 15/07/2010(UTC)Posts: 330Location: Beer-ShevaWas thanked: 425 time(s) in 230 post(s) Graph of implicit function with bifurcation point (Problem onthe calculation of the arch)https://en.smath.info/forum/yaf_...thod-in-Engineering.aspxThe graph consists of three curves that occur at the bifurcation point.1. Find the coordinates of the bifurcation point2.The starting point for each of the three graphs is taken near the bifurcation point3. Build graphics by Draghilev method Point Bifurcation.sm (39kb) downloaded 20 time(s). 1 user thanked Ber7 for this useful post. on 24/11/2018(UTC)
 Jean Giraud #48 Posted : 26 November 2018 04:29:54(UTC) Rank: Advanced MemberGroups: Registered Joined: 04/07/2015(UTC)Posts: 4,307Was thanked: 751 time(s) in 592 post(s) Originally Posted by: Ber7 The graph consists of three curves that occur at the bifurcation point.1. Find the coordinates of the bifurcation point2.The starting point for each of the three graphs is taken near the bifurcation point3. Build graphics by Draghilev methodThanks Ber7.This version works fine compared to the previous "arca" that never stopped pedaling .By same token, I'm puzzled by the Lagrange points. Where those contours come from ?
 frapuano #49 Posted : 26 November 2018 10:56:38(UTC) Rank: Advanced MemberGroups: Registered Joined: 01/08/2010(UTC)Posts: 115Location: RomeWas thanked: 13 time(s) in 13 post(s) Joan from Wikipedia it is stated that they are involved in Astronomy and that for 2 large bodies there are 5 of these points so I guess that your pictures/worksheet refers on how to calculate them all(their positions).https://en.wikipedia.org/wiki/Lagrangian_pointBest regardsFranco
 Jean Giraud #50 Posted : 28 November 2018 16:30:11(UTC) Rank: Advanced MemberGroups: Registered Joined: 04/07/2015(UTC)Posts: 4,307Was thanked: 751 time(s) in 592 post(s) Originally Posted by: Ber7 Thank you, Alvaro. The norme function simplifies the code and reduces the calculation time.Example of using norme when solving ODEdn_GearsBDF is nearly ½ time. I think its Lorentz
 алексей_алексей #51 Posted : 05 January 2019 16:22:29(UTC) Rank: MemberGroups: Registered Joined: 30/09/2012(UTC)Posts: 27Was thanked: 10 time(s) in 5 post(s) Maple, Draghilev's method. The inverse problem of kinematics. For those who want to try hard and to do better in SMath.
 Jean Giraud #52 Posted : 05 January 2019 18:10:14(UTC) Rank: Advanced MemberGroups: Registered Joined: 04/07/2015(UTC)Posts: 4,307Was thanked: 751 time(s) in 592 post(s) Originally Posted by: алексей_алексей hose who want to try hard and to do better in SMath.Thanks for the suggestion. My head is not oblate like Extraterrestrials !
 Ber7 #53 Posted : 06 January 2019 11:18:45(UTC) Rank: Advanced MemberGroups: Registered Joined: 15/07/2010(UTC)Posts: 330Location: Beer-ShevaWas thanked: 425 time(s) in 230 post(s) Originally Posted by: Razonar . I don't remember to read nothing in the literature about equally spaced points in the numerical solution of the ode, except for the opposite: adaptive steps, but referring for the time variable, not the X,Y,Z solution points. About how you apparently get the same distance between solution points, i.e. sqrt(X^2+Y^2+Z^2), I guess that the background theory must to be in the Draghilev method and how the solution (X,Y,Z) is obtained from the differential equation. You have a very interesting point for investigate and publish about it.Apparently the distance between the points is 1 (guess can be easily proved because you divide by the norme the system), and this seems to provide more stable numerical solutions for the system (can be applied here Lyapunov's theorems?)Best regards.Alvaro.An article about the effectiveness of the solution of the system diff. equations for parameterization integral curve through arc length Russiy.pdf (608kb) downloaded 34 time(s). 2 users thanked Ber7 for this useful post. on 06/01/2019(UTC),  on 07/01/2019(UTC)
 Razonar #54 Posted : 09 January 2019 00:02:47(UTC) Rank: Advanced MemberGroups: Registered Joined: 28/08/2014(UTC)Posts: 445Was thanked: 254 time(s) in 155 post(s) Originally Posted by: Ber7 Originally Posted by: Razonar . I don't remember ... An article about the effectiveness of the solution of the system diff. equations for parameterization integral curve through arc length Russiy.pdf (608kb) downloaded 34 time(s).Thanks for the paper. Now you found the keywords for this point, which seems to be "Arc Length Method". This give only 79 results at google search:Results are related with mechanical engineering for finite elements analysis. From the first result, having this attached file: https://scholar.harvard....sios/files/ArcLength.pdf But actually I don't find any appointment nor observation that solution points are equally spaced. Notice that It could be some "obvious" point for, given f(t,x,x' ) = 0, plot for x(t) it's equally spaced if one transform it to f(s,x,x' ) with s as the arc length. But it's immediate for me that the plot for the state space (x,x' ) seems to be equally spaced too, as in some smath examples here in this topic.Also, for the observation that can apply Lyapunov theorems about stability of solutions, there are some references in the 79 google's search results. The application here of Lyapunov is related about the stability of the found solutions, because authors using the parametrization along the arc length for ill conditioned systems.Originally Posted by: Razonar . Apparently the distance between the points is 1 (guess can be easily proved because you divide by the norme the system), and this seems to provide more stable numerical solutions for the system (can be applied here Lyapunov's theorems?)Best regards.Alvaro.Edited by user 09 January 2019 00:15:12(UTC)  | Reason: Not specified 2 users thanked Razonar for this useful post. on 09/01/2019(UTC),  on 09/01/2019(UTC)
 Ber7 #55 Posted : 26 February 2019 20:32:50(UTC) Rank: Advanced MemberGroups: Registered Joined: 15/07/2010(UTC)Posts: 330Location: Beer-ShevaWas thanked: 425 time(s) in 230 post(s) Finding Minimum Distanceof a Point from Curve (with Draghilev method) MinDistDragilev.sm (24kb) downloaded 21 time(s).Edited by user 27 February 2019 11:55:44(UTC)  | Reason: Not specified 4 users thanked Ber7 for this useful post. on 26/02/2019(UTC),  on 26/02/2019(UTC),  on 26/02/2019(UTC),  on 25/03/2019(UTC)
 Jean Giraud #56 Posted : 26 February 2019 21:07:47(UTC) Rank: Advanced MemberGroups: Registered Joined: 04/07/2015(UTC)Posts: 4,307Was thanked: 751 time(s) in 592 post(s) Originally Posted by: Ber7 Finding Minimum Distance of a Point from CurveThanks Ber7 ... works fine.
 Ber7 #57 Posted : 13 March 2019 20:47:37(UTC) Rank: Advanced MemberGroups: Registered Joined: 15/07/2010(UTC)Posts: 330Location: Beer-ShevaWas thanked: 425 time(s) in 230 post(s) Distance from point to implicit curve(with al_nleqsolve)A thick red line is the normal to the curve at point a. FindDist.pdf (244kb) downloaded 21 time(s). FindDist.sm (73kb) downloaded 24 time(s). 4 users thanked Ber7 for this useful post. on 13/03/2019(UTC),  on 13/03/2019(UTC),  on 13/03/2019(UTC),  on 25/03/2019(UTC)
 Ber7 #58 Posted : 24 March 2019 19:53:07(UTC) Rank: Advanced MemberGroups: Registered Joined: 15/07/2010(UTC)Posts: 330Location: Beer-ShevaWas thanked: 425 time(s) in 230 post(s) Refined the algorithm and added examples DistMod.sm (52kb) downloaded 19 time(s). 3 users thanked Ber7 for this useful post. on 24/03/2019(UTC),  on 24/03/2019(UTC),  on 25/03/2019(UTC)
 Jean Giraud #59 Posted : 25 March 2019 00:18:49(UTC) Rank: Advanced MemberGroups: Registered Joined: 04/07/2015(UTC)Posts: 4,307Was thanked: 751 time(s) in 592 post(s) Originally Posted by: Ber7 Refined the algorithm and added examplesThanks Ber7, looks interesting but couldn't doctor SS 6179.
 Ber7 #60 Posted : 25 March 2019 14:19:26(UTC) Rank: Advanced MemberGroups: Registered Joined: 15/07/2010(UTC)Posts: 330Location: Beer-ShevaWas thanked: 425 time(s) in 230 post(s) How the algorithm works. Each time you press F9, we set the new position of point A Animat.sm (22kb) downloaded 16 time(s).Edited by user 25 March 2019 14:22:16(UTC)  | Reason: Not specified 2 users thanked Ber7 for this useful post. on 25/03/2019(UTC),  on 25/03/2019(UTC)
 Users browsing this topic
 Similar Topics Draghilev method revisited [Isocurves] (Samples) by Jean Giraud 27/03/2019 18:17:33(UTC)
 4 Pages<1234>
Forum Jump
You cannot post new topics in this forum.
You cannot reply to topics in this forum.
You cannot delete your posts in this forum.
You cannot edit your posts in this forum.
You cannot create polls in this forum.
You cannot vote in polls in this forum.