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.

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).

Thank you very much.
Cheers

Wrote

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.

... here is an example:

ODE Lorenz Attractor Publish.sm (15,19 KiB) scaricato 1360 volta(e).

Hi, the differential equations that i should solve are like the ones in the picture:



here is also the .sm file… Documento2 DE.sm (21,27 KiB) scaricato 1323 volta(e).

Wrote

here is also the .sm file

φ''(t) ... is not defined

Documento2 DE.sm (25,19 KiB) scaricato 1371 volta(e).

Alvaro has done lot of work on that one, few days ago
it was about tangent, curvature ... As it look: same system.

... revisit your original document 11 days ago.
revisit Alvaro reply.

curvatura (1 doctored).sm (53,54 KiB) scaricato 1357 volta(e).

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.

Wrote

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 (33,26 KiB) scaricato 1076 volta(e).

Why should i define the phi function?
Should I get it by solving the differential equation, or am I wrong?

Wrote

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 (66,82 KiB) scaricato 1103 volta(e).

... a short revisit.

ODE Compendium_1.sm (154,96 KiB) scaricato 1298 volta(e).

... that's as far as I can make this project respond.
Not enough insight to go further.

Page57 ODE.sm (12,74 KiB) scaricato 1475 volta(e).

Wrote

... 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 (45,25 KiB) scaricato 1120 volta(e).

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

Wrote

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 (48,35 KiB) scaricato 1135 volta(e).

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?

Wrote

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 ?

Does the CannonBall project suggest something ?

Maths Cannonball.sm (29,33 KiB) scaricato 1375 volta(e).