# Scaling Independent Variables in Composed \`ODESystem\`s

**URL:** <https://discourse.julialang.org/t/scaling-independent-variables-in-composed-odesystem-s/103431>\
**Category:** Modelling & Simulations\
**Tags:** question, package, modelingtoolkit\
**Created:** [September 1, 2023, 1:55am UTC](https://discourse.julialang.org/t/scaling-independent-variables-in-composed-odesystem-s/103431 "2023-09-01T01:55:01Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![cadojo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/cadojo/32/25328_2.png) [@cadojo](https://discourse.julialang.org/u/cadojo)\
**Post date:** [September 1, 2023, 1:55am UTC](https://discourse.julialang.org/t/scaling-independent-variables-in-composed-odesystem-s/103431/1 "2023-09-01T01:55:02Z")

</div>

I have code that implements the nondimensional form of a simplified three-body problem. The length units are scaled by the distance between the two celestial bodies, `a`, and the time units are scaled by the orbital period of the two bodies, `T`, about their common center of mass.

I have the nondimensional form as an `ODESystem`. A simplified system is shown below in `f`. Now I’m trying to implement the _dimensioned_ system, which scales all of the variables appropriately, as in `g`. So `g.x ~ f.x / a`. That works fine.

But `f` and `g` have different independent variables… specifically, the independent variable in `f` is equivalent to the independent variable in `g` **divided by `T`**.

Is this possible to do? Can I relate one system’s `iv` to another’s? The goal here is for the user to never have to interact with nondimensioned units. They can specify initial conditions in the dimensioned units, and under the hood `structural_simplify` scales the conditions and dynamics.

I can accomplish all of this by pasting the equations of `f` inline within `g`, as opposed to composing the two systems, but I was wondering if there’s a way to do this through model composition.

```julia
using ModelingToolkit

function f()
   @parameters t p
   @variables x(t)
   d = Differential(t)
   
   return ODESystem([d(x) ~ -p * x], t, [x], [p]; name=:f)
end

function g()
   @parameters τ p₁ p₂ a
   @variables x(τ)
   
   T = 2π * sqrt(a^3 / (p₁+p₂))
   s = f()
   return compose(ODESystem([s.p ~ p₂ / (p₁+p₂), x ~ a * s.x, s.t ~ τ / T], τ, [x], [p₁, p₂, a]; name=:g), s)
end

```

```julia
g()
ERROR: ArgumentError: System f: variable t does not exist
Stacktrace:
 [1] getvar(sys::ODESystem, name::Symbol; namespace::Bool)
   @ ModelingToolkit ~/.julia/packages/ModelingToolkit/FbXPg/src/systems/abstractsystem.jl:358
 [2] getvar
   @ ~/.julia/packages/ModelingToolkit/FbXPg/src/systems/abstractsystem.jl:311 [inlined]
 [3] getproperty(sys::ODESystem, name::Symbol; namespace::Bool)
   @ ModelingToolkit ~/.julia/packages/ModelingToolkit/FbXPg/src/systems/abstractsystem.jl:309
 [4] getproperty
   @ ~/.julia/packages/ModelingToolkit/FbXPg/src/systems/abstractsystem.jl:308 [inlined]
 [5] g()
   @ Main ./REPL[8]:7
 [6] top-level scope
   @ REPL[10]:1

```

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<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [September 12, 2023, 5:34pm UTC](https://discourse.julialang.org/t/scaling-independent-variables-in-composed-odesystem-s/103431/2 "2023-09-12T17:34:39Z")

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Right now you can only compose systems with the same independent variable, but I think with an equation relating independent variables it would be possible in theory, so open an issue as this might be a fun project down the line.