@@ -4,9 +4,9 @@ ModelingToolkit has a system for transformations of mathematical
4
4
systems. These transformations allow for symbolically changing
5
5
the representation of the model to problems that are easier to
6
6
numerically solve. One simple to demonstrate transformation is the
7
- ` structural_simplify ` with does a lot of tricks, one being the
8
- transformation that sends a Nth order ODE
9
- to a 1st order ODE .
7
+ ` structural_simplify ` , which does a lot of tricks, one being the
8
+ transformation that turns an Nth order ODE into N
9
+ coupled 1st order ODEs .
10
10
11
11
To see this, let's define a second order riff on the Lorenz equations.
12
12
We utilize the derivative operator twice here to define the second order:
@@ -26,12 +26,12 @@ eqs = [D(D(x)) ~ σ * (y - x),
26
26
```
27
27
28
28
Note that we could've used an alternative syntax for 2nd order, i.e.
29
- ` D = Differential(t)^2 ` and then ` E (x)` would be the second derivative,
29
+ ` D = Differential(t)^2 ` and then ` D (x)` would be the second derivative,
30
30
and this syntax extends to ` N ` -th order. Also, we can use ` * ` or ` ∘ ` to compose
31
31
` Differential ` s, like ` Differential(t) * Differential(x) ` .
32
32
33
33
Now let's transform this into the ` ODESystem ` of first order components.
34
- We do this by simply calling ` ode_order_lowering ` :
34
+ We do this by calling ` structural_simplify ` :
35
35
36
36
``` @example orderlowering
37
37
sys = structural_simplify(sys)
0 commit comments