Drasil Research Group Meeting Agenda, 1:30 pm, Friday May 20, 2022 (On Teams)

[smiths]

The agenda for this coming week is as follows:

1. Dong update
2. Peter update
3. Jason update
4. Org Mode for Literate Programming
5. Cold cases
   a. @peter-michalski SWHS Body, Hardcoded Names #1848
   b. @balacij - Allow for different authors between documents #1804
   c. @cd155 Implement "unmodular" option for code generation #1999
6. Questions/Comments/Concerns/Discussion

[cd155]

A follow-up on today's meeting.

I think Dr.@smiths mentioned there might be some problems with solving the double pendulum example, but I didn't remember exactly what. Is that be ok to say it again, so I can re-evaluate the solution.

[cd155]

If we have the following equations, we can solve it as the initial value problem by giving four initial values, for example

θ₁ = 30 degree
ω₁= 5 degree/s
θ₂ = 60 degree
ω₂ = 25 degree/s

other values, like m₁, m₂, L₁, L₂, and g are given, so I think we have enough information.

[smiths]

My question was about whether you depend on being able to represent the system of ODEs in matrix form. Although the system of equations above is definitely solvable using the external libraries, you cannot represent it in matrix form because the dependent variables aren't isolated. You don't have a linear ODE in this case.

As long as the matrix form is required this isn't a problem.

[cd155]

I see, thanks for bringing it up. That's certainly a problem in there because we ask users to put coefficient and dependent variables in a matrix form.

Basically, this form cannot be entered in a matrix form. In the long term, do you think is there any potential solution to this problem?

[JacquesCarette]

Some solvers allow "black boxes" as input, to represent arbitrary functions of the dependent variables. We should be guided by the solvers themselves as to what to do here. I forget the details.

Note that for the pendulum, if the sin/cos addition laws are used, then if new variables for sin(theta_1), cos(theta_1), etc are added (and relations between them), it can be written as a large ODE system

[smiths]

@cd155, I agree with the reply from @JacquesCarette. Writing a linear system of ODEs in matrix form is actually a fairly special case. It comes up frequently in practice, but there are also plenty of more complex examples. There are algorithms that can solve linear systems quickly and efficiently, but there are also algorithms for the more general case. As long as we can write the differential equations in an explicit form, it should be possible to solve them with one of our libraries.