I THINK that the single shooter is ok. I can always improve it later

julia/single_shoot.jl

@@ -0,0 +1,33 @@
+using NLsolve
+
+function treat_inputs(x::AbstractVector, n::Int)
+  inputs = reshape(copy(x),(3,n))'
+  for i in 1:n
+    inputs[i,1] = 0.5*tanh(inputs[i,1]) + 0.5
+    inputs[i,2] = π*tanh(inputs[i,2])
+    inputs[i,3] = π*tanh(inputs[i,3])/2
+  end
+  return inputs
+end
+
+function single_shoot(start::Vector{Float64},
+                      final::Vector{Float64},
+                      craft::Sc,
+                      μ::Float64,
+                      t0::Float64,
+                      tf::Float64,
+                      n::Int,
+                      x0::AbstractVector,
+                      tol=1e-2)
+
+  function f!(F,x)
+    F[1:6] .= prop(treat_inputs(x,n), start, craft, μ, tf-t0)[1][end,:] - final
+    F[7:3n] .= 0.
+    # if typeof(F[1]) == Float64 println(F[1:6]) end
+    # if typeof(F[1]) == Float64 println(treat_inputs(x,n)[1:8,1]) end
+    
+  end
+
+  return nlsolve(f!, x0, ftol=tol, autodiff=:forward, iterations=10_000)
+
+end