Merge pull request #63 from JuliaGNI/fix_coupled_oscillator_docs

Fixed docs (not using GML now).

docs/src/coupled_harmonic_oscillator.md

@@ -2,6 +2,54 @@
 
 This system describes two harmonic oscillators that are coupled nonlinearly. 
 
+```@example
+HTML("""<object type="image/svg+xml" class="display-light-only" data=$(joinpath(Main.buildpath, "images/coupled_harmonic_oscillator.png"))></object>""") # hide
+```
+
+```@example
+HTML("""<object type="image/svg+xml" class="display-dark-only" data=$(joinpath(Main.buildpath, "images/coupled_harmonic_oscillator_dark.png"))></object>""") # hide
+```
+
+The following shows the ``q_1`` component of the system for different values of ``k``: 
+
+```@eval
+using GeometricIntegrators: integrate, ImplicitMidpoint 
+using GeometricProblems.CoupledHarmonicOscillator: hodeproblem, default_parameters
+using Plots 
+ 
+const m₁ = default_parameters.m₁  
+const m₂ = default_parameters.m₂ 
+const k₁ = default_parameters.k₁ 
+const k₂ = default_parameters.k₂ 
+const k = [0.0, 0.5, 0.75, 1.0, 2.0, 3.0, 4.0] 
+ 
+params_collection = [(m₁ = m₁, m₂ = m₂, k₁ = k₁, k₂ = k₂, k = k_val) for k_val in k] 
+problems = [hodeproblem(; params = params_collection[i]) for i in axes(k, 1)] 
+ensemble_solution = [integrate(problem, ImplicitMidpoint()) for problem in problems]
+ 
+t = ensemble_solution[1].t
+
+q₁ = zeros(1, length(t), length(k))
+
+for index in axes(k, 1)
+    q₁[1, :, index] =  ensemble_solution[index].q[:, 1]
+end
+
+n_param_sets = length(params_collection) #hide 
+labels = reshape(["k = "*string(params.k) for params in params_collection], 1, n_param_sets) 
+ 
+q₁ = q₁[1, :, :]
+const one_plot = false 
+const psize = (900, 600) 
+plot_q₁ = one_plot ? plot(0.0:0.4:100.0, q₁, size=psize) : plot(0.0:0.4:100.0, q₁, layout=(n_param_sets, 1), size=psize, label=labels, legend=:topright)
+
+png(plot_q₁, "q_component")
+
+nothing
+```
+
+![](q_component.png)
+
 
 ## Library functions