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Hello everyone! I wanted to know if it is possible to solve differential equations with Smath Studio. in particular I would be interested in solving ordinary nonlinear second order differential equations.
Thanks in advance.
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In the interactive handbook (see Tools> Plugins> Interactive books (switch to online gallery)) there is a section
Mathematics> Ordinary Differential Equations.
In the examples subsection you find a variety of non-linear ODEs with numerical and symbolic solutions (based on Maxima plugin). |
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Thank you very much.
Cheers
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Originally Posted by: Ale16595  Hello everyone! I wanted to know if it is possible to solve differential equations with Smath Studio. in particular I would be interested in solving ordinary nonlinear second order differential equations.
Thanks in advance. Please: attach DE.
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Hi, the differential equations that i should solve are like the ones in the picture:  here is also the .sm file…  Documento2 DE.sm (22kb) downloaded 45 time(s).
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Originally Posted by: Ale16595 here is also the .sm file φ''(t) ... is not defined Documento2 DE.sm (26kb) downloaded 52 time(s).Alvaro has done lot of work on that one, few days ago it was about tangent, curvature ... As it look: same system.
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Yes, the problem is the same as a few days ago. This time, however, I had to modify it slightly and I must be able to derive the psi and phi functions using the differential equations in the figure.
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Originally Posted by: Ale16595 Hi, the differential equations that i should solve are like the ones in the picture: ... still undefined wrt φ'(t) If you can help more: please re-post this document so to avoid refactoring. If you have the original work out and solution it might help converting to Smath Documento2 DE [explain more].sm (34kb) downloaded 46 time(s).
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Why should i define the phi function?
Should I get it by solving the differential equation, or am I wrong?
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Originally Posted by: Ale16595 Why should i define the phi function?
Should I get it by solving the differential equation, or am I wrong? You are right, after the numerical ODE solver you will have the manipulate the solution depending upon sin/cos The 2nd term is not a simple coefficient. That induces FinDiff. So, you have nothing from source ? Pure invention top/bottom. Documento2 DE [explain more].sm (67kb) downloaded 28 time(s).
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... that's as far as I can make this project respond. Not enough insight to go further. Page57 ODE.sm (13kb) downloaded 45 time(s).
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Originally Posted by: Jean Giraud ... that's as far as I can make this project respond.
Not enough insight to go further.
... your original parameters send the DE solutions in the zillion domain. Zillion domain is no maths, something does not cut the mustard in there. Better sanity with other CAS ... Documento2 DE [explain more].sm (46kb) downloaded 25 time(s).
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Hi, thanks for the help and patience.
This is a task I have been assigned and I am not following any source.
If it can be helpful to derive the function phi, I know that:
-for t=0, phi=0
-for t=6.187, phi=0.867 and phi'=0
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Originally Posted by: Ale16595 Hi, thanks for the help and patience.
This is a task I have been assigned and I am not following any source.
If it can be helpful to derive the function phi, I know that:
-for t=0, phi=0
-for t=6.187, phi=0.867 and phi'=0 ================================= -for t=6.187, phi=0.867 and phi'=0 we have that from freaking p1 parameter and obviously phi'=0 for t=0, phi=0 ...that can't be whereas the system starts @ IC 0.005 1. Make sure the DE as proposed is OK 2. What software the presumed assignment is based on ? ... it could be wrong from the onset !!! Documento2 DE [explain more].sm (49kb) downloaded 22 time(s).
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I modified some values and a relationship because I noticed an error. The differential equation, on the other hand, should be correct because it comes out of the physical problem it is trying to solve. As for the assignment of values, I always get them from the physical system knowing more or less the trend of the phi function to be obtained. If it can help the progress of this function it is the following: -The phi function starts from 0.147 for t = 0, grows up to a maximum equal to 0.867 for t = 6.187 and finally decreases -The function phi' instead starts from a value 0 for t = 0, in the interval between t = 0 and t = 6.187 reaches a maximum and then returns to 0 when t = 6.187 Then I would have a question, why does phi' appear in the differential equation and not phi? 
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Originally Posted by: Ale16595 Then I would have a question, why does phi' appear in the differential equation and not phi? Good question: you are the Man who proposed the DE phi'. For your above attempted explanation, you are just presuming. 1. Setup the DE ... as per the assignment 2. Confirm the reference solver software the Originator is using. Will be back while waiting. The project is pure blue sky ... sending a fly to Cirus ?
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Does the CannonBall project suggest something ? Maths Cannonball.sm (30kb) downloaded 67 time(s).
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