# Problem with using the results of ParametricNDSolve in a ParametricPlot3D

I new to Mathematica and I have a problem with certain equations. I want to plot a trajectory in spherical coordinates given by the equations:

(1 + α^2)*(Abs[γ])^-1*θ'[t] == (Sin[2*θ[t]]*Subscript[H, d]*α)/
2 + ((Cos^2)[ϕ[t]]*Sin[2*θ[t]]*α - Sin[2*ϕ[t]]*Sin[θ[t]])*Subscript[H, k]/
2 - (α*M*(Cos[β]*Cos[θ[t]]*Cos[ϕ[t]] - Sin[β]*Sin[θ[t]]) +
M*Cos[β]*Sin[ϕ[t]])*Subscript[α, j]


and

(1 + α^2)*(Abs[γ])^-1*ϕ'[t] == -Cos[θ[t]]*Subscript[H, d]*α - (2*(Cos^2)[ϕ[t]]*Cos[θ[t]] -
α*Sin[2*ϕ[t]])*Subscript[H, k]/2 - Cos[θ[t]]*(α*M*(Cos[β]*Cos[θ[t]]*Cos[ϕ[t]] -
Sin[β]*Sin[θ[t]]) -
M*Cos[β]*Sin[ϕ[t]])*Subscript[α, j]


My (crude) code is:

sol = ParametricNDSolve[{(1 + α^2)*(Abs[γ])^-1*θ'[t] == (Sin[2*θ[t]]*Subscript[H, d]*α)/
2 + ((Cos^2)[ϕ[t]]*Sin[2*θ[t]]*α - Sin[2*ϕ[t]]*Sin[θ[t]])*Subscript[H, k]/
2 - (α*M*(Cos[β]*Cos[θ[t]]*Cos[ϕ[t]] - Sin[β]*Sin[θ[t]]) +
M*Cos[β]*Sin[ϕ[t]])*Subscript[α, j], (1 + α^2)*(Abs[γ])^-1*ϕ'[t] ==
-Cos[θ[t]]*Subscript[H, d]*α - (2*(Cos^2)[ϕ[t]]*Cos[θ[t]] - α*
Sin[2*ϕ[t]])*Subscript[H, k]/2 -
Cos[θ[t]]*(α*M*(Cos[β]*Cos[θ[t]]*Cos[ϕ[t]] - Sin[β]*Sin[θ[t]]) -
M*Cos[β]*Sin[ϕ[t]])*Subscript[α, j], ϕ[0] == 0, θ[0] == 0},
{ϕ[t], θ[t]}, {t, 0, 100},
{α, Subscript[H, d], Subscript[α, j], Subscript[H, k], M, γ, β}]


and I try to plot it:

ParametricPlot3D[
Evaluate[{M*Cos[ϕ[t]]*Sin[θ[t]] /. sol,
M*Sin[ϕ[t]]*Sin[θ[t]] /. sol,
M*Cos[θ[t]] /. sol} /. {α -> 1,
Subscript[H, d] -> 1, Subscript[α, j] -> 1,
Subscript[H, k] -> 1, M -> 1, γ -> .1, β -> .1}, {t,
0, 100}]]


but the plot isn't displayed and I don't get any errors. Does anyone know what am I doing wrong? Thanks in advance!

-
Have you actually looked at what Evaluate[{M*Cos[ϕ[t]]*Sin[θ[t]] /. sol, M*Sin[ϕ[t]]*Sin[θ[t]] /. sol, M*Cos[θ[t]] /. sol} /. {α -> 1, Subscript[H, d] -> 1, Subscript[α, j] -> 1, Subscript[H, k] -> 1, M -> 1, γ -> .1, β -> .1} is feeding to ParametricPlot3D? Is it what you expect? –  m_goldberg May 13 '14 at 2:24