Why doesn't my Manipulate expression work?

Question

I want to change 3 parameters: Subscript[I, dc], Subscript[B, dc], Subscript[μM, 0] and see changing on 2 graphs:

Plot[Evaluate[mx[t] /. s1], {t, 0, 50}, AxesLabel -> {t, mx}]

and

ParametricPlot3D[Evaluate[m[t] /. s1], {t, 0, 50}, PlotRange -> Full]

My code:

m[t_] := {mx[t], my[t], mz[t]}

γ = 28;

h = 6.62*10^-34;

e = 1.6*10^-19;

Subscript[μ, 0] = 1.25*10^-6;

Subscript[μM, 0] = 800*10^-3;

Subscript[M, 0] = 0.64*10^6;

Subscript[r, 0] = 100*10^-9;

Subscript[l, 0] = 3*10^-9;

Subscript[I, dc] = 1*10^-3;

Subscript[B, dc] = 200*10^-3;

Subscript[α, G] = 0.01;

p = {0, 0, 1};

σ =(γ*h/2*e)*1/(Subscript[M, 0]*Pi*(Subscript[r, 0])^2)*Subscript[l, 0];

Subscript[B, eff] = {Subscript[B, dc], 0, 0}-Subscript[μM, 0]*(m[t]*p);

system1 ={D[m[t], t] ==γ*(Cross[Subscript[B, eff], m[t]]) + Subscript[α, G]*(Cross[m[t], D[m[t], t]]) +σ*Subscript[I, dc]*(Cross[m[t], Cross[m[t], p]]),(m[t] /. t -> 0) == {0, 1, 0}};

s1 = NDSolve[system1, m[t], {t, 0, 50}]

Plot[Evaluate[{mx[t], my[t], mz[t]} /. s1], {t, 0, 50},AxesLabel -> {t, m}]

Plot[Evaluate[mx[t] /. s1], {t, 0, 50}, AxesLabel -> {t, mx}]

ParametricPlot3D[Evaluate[m[t] /. s1], {t, 0, 50}, PlotRange -> Full]

I tried to use "Manipulate" but have mistakes and it's not working. Below, how i tried to use "Manipulate"

Manipulate[
  Plot[Evaluate[mx[t] /. s1], {t, 0, 50}, AxesLabel -> {t, mx}], 
  {Subscript[I, dc], 0.001, 100}]

The error message I get is:

Manipulate::vsform: Manipulate argument {Subscript[I, dc],0.001,100} does not have the correct form for a variable specification.

general topic 107628 and probably a duplicate: 85023, do you agree? — Kuba, Mar 05 '17 at 19:06
do not use Subscript. Subscript should really be removed from future version of Mathematica :) — Nasser, Mar 05 '17 at 19:18
I'm voting to close this question as off-topic because it is too localized; i.e, it applies only to the local situation and needs of its poster and answers will not benefit others. — m_goldberg, Mar 05 '17 at 21:35

m_goldberg · Answer 1 · 2017-03-05T22:40:52.220

As the message you are seeing is telling you, the form Subscript[...] is not allowed as a control variable name in a Manipulate expression. AFAIK only identifiers that would be accepted as variable names in a list of local variable specifications given to DynamicModule can be used.

However, your code wouldn't work even if you were to rename your subscripted variables to ordinary variables. You would still face the fundamental problem that the parameters, such as Subscript[I, dc], have all been replaced by numerical values by the time NDSolve is evaluated.

Manipulate can only vary parameters in an expression that appear as symbols. You have no symbolic parameters in the plot expression you give to Manipulate. You just have a static plot where nothing can be varied.

You can see this by removing the semi-colon at the end of the expression the compute system1.

Why doesn't my Manipulate expression work?

1 Answers1