# How can I define a vector in ModelingToolkit

**URL:** <https://discourse.julialang.org/t/how-can-i-define-a-vector-in-modelingtoolkit/107278>\
**Category:** Modelling & Simulations\
**Tags:** question, package, modelingtoolkit\
**Created:** [December 7, 2023, 3:13pm UTC](https://discourse.julialang.org/t/how-can-i-define-a-vector-in-modelingtoolkit/107278 "2023-12-07T15:13:00Z")\
**Posts on this page:** 1\
**Showing post:** 6

<div class="post-metadata">

**Author:** ![RobbesU](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/robbesu/32/212459_2.png) [@RobbesU](https://discourse.julialang.org/u/RobbesU)\
**Post date:** [January 29, 2025, 11:12am UTC](https://discourse.julialang.org/t/how-can-i-define-a-vector-in-modelingtoolkit/107278/6 "2025-01-29T11:12:55Z")

</div>

Above code block doesn’t work anymore under `ModelingToolkit v9.61.0` (Julia 1.11.3) but works with a few adjustments.

```julia
duration = 5.0
tspan = (0.0, duration)
dt = 0.02
ts = 0:dt:duration
	
G_EARTH = Float64[0.0, -0.0, -9.81] # gravitational acceleration
G_MOON = G_EARTH * 0.166
	
# model
@variables (pos(t))[1:3] = [0.0, 0.0, 0.0] # defaults to 'at rest at origin'
@variables (vel(t))[1:3] = [0.0, 0.0, 0.0] 
@variables (acc(t))[1:3] # NO defaults as balanced by force!

@parameters (force)[1:3] # do not provide default or structural_simplify will remove eqs where f=0 !
	
eqs = [
	collect( D.(pos) .~ vel )... # .~ instead of just ~ !
	collect( D.(vel) .~ acc )...
    collect( acc .~ force )...
]
	
@named sys = ODESystem(eqs, t)
simple_sys = structural_simplify(sys)
	
u0 = [pos=>[0.,0.,0.], vel=>[0.,0.,+10.0] ] # MTK unknows are pos & vel: unknowns(simple_sys) 
p0 = [[0.,0.,-9.81]] # [G_EARTH] 

prob = ODEProblem(simple_sys, u0, tspan, p0)
sol = solve(prob, Rodas5(), dt=dt, saveat=ts)
plot(sol)

```

When constructing as a component block it becomes as follows (I added a force as well as default gravity). Note the requirement to state the initial condition keys as symbolic `:pos` and `:vel` if using the Dict version of `u0`:

```julia
# model as component
@component function TestMass3D(;name, m, g=G_EARTH)
	
	vars = @variables begin
		(pos(t))[1:3] = [0.0, 0.0, 0.0] # defaults to 'at rest at origin'
		(vel(t))[1:3] = [0.0, 0.0, 0.0] 
		(acc(t))[1:3] # NO defaults as balanced by force!
	end
		
	pars = @parameters (force)[1:3] # do not provide default or structural_simplify will remove eqs where f=0 !
	
	eqs = [
		collect( D.(pos) .~ vel )...
		collect( D.(vel) .~ acc )...
	    collect( acc .~ force./m .+ g )...
	]

	return ODESystem(eqs, t, vars, pars;name)
end

@named sys = TestMass3D(m=1, g= G_MOON)
simple_sys = structural_simplify(sys)
	
u0 = [:pos=>[0.,0.,0.], :vel=>[0.,0.,+10.0] ] # MTK unknows are pos & vel: check with unknowns(simple_sys) 
p0 = [[0.,0.,+2.] ] # note vector inside array as only 1 parameter 

prob = ODEProblem(simple_sys, u0, tspan, p0)

sol = solve(prob, Rodas5(), dt=dt, saveat=ts)
plot(sol)

```

(this also links with [https://discourse.julialang.org/t/broadcast-inside-of-mtkmodel-macro-causes-precompilation-failures-when-put-into-a-package/107277/18](https://discourse.julialang.org/t/broadcast-inside-of-mtkmodel-macro-causes-precompilation-failures-when-put-into-a-package/107277/18)

---

_[View the full topic](https://discourse.julialang.org/t/how-can-i-define-a-vector-in-modelingtoolkit/107278)._