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differential equations - Numerical resolution of non-linear coupled ODEs


I have problem with my code in Mathematica. I have introduced the set of coupled non-linear ODES. This is the resolution part:


(*Initial parameters*)
A = 0.5;
a = 0.9;
Ω = 0.24;


(*Initial conditions*)
Ï…0 = 0.22;
α0 = Pi;
ψ0 = Pi/2;
r0 = 20;
θ0 = Pi/8;
φ0 = 0;

Needs["DifferentialEquations`NDSolveProblems`"]; \
Needs["DifferentialEquations`NDSolveUtilities`"];

(*Systems to integrate*)

system = {x1'[t] == 
    Eq1[A, a, Ω, x1[t], x2[t], x3[t], x4[t], x5[t]],
   x2'[t] == 
    Eq2[A, a, Ω, x1[t], x2[t], x3[t], x4[t], x5[t]],
   x3'[t] == 
    Eq3[A, a, Ω, x1[t], x2[t], x3[t], x4[t], x5[t]],
   x4'[t] == 
    Eq4[A, a, Ω, x1[t], x2[t], x3[t], x4[t], x5[t]],

   x5'[t] == 
    Eq5[A, a, Ω, x1[t], x2[t], x3[t], x4[t], x5[t]],
   x6'[t] == 
    Eq6[A, a, Ω, x1[t], x2[t], x3[t], x4[t], x5[t]], 
   x1[0] == υ0, x2[0] == α0, x3[0] == ψ0, 
   x4[0] == r0, x5[0] == θ0, x6[0] == φ0};

sol = NDSolve[system, {x1, x2, x3, x4, x5, x6}, {t, 0, 14000}, 
   Method -> {"StiffnessSwitching", 
     Method -> {"ExplicitRungeKutta", Automatic}}, AccuracyGoal -> 22,

    MaxSteps -> Infinity, PrecisionGoal -> 15, WorkingPrecision -> 22];

ParametricPlot3D[
 Evaluate[{x4[t]*Sin[x5[t]]*Cos[x6[t]], x4[t]*Sin[x5[t]]*Sin[x6[t]], 
    x4[t]*Cos[x5[t]]} /. sol], {t, 0, 14000}, PlotPoints -> 10000, 
 ColorFunction -> {Red}, ImageSize -> 500]

I receive the following error messages



NDSolve::precw: "The precision of the differential equation ({<<1>>}) is less than \ WorkingPrecision (22.`)"

NDSolve::ndsz: At t == 140.91450584595810589848638366914914657367`22., step size is \ effectively zero; singularity or stiff system suspected



Someone could suggest me how to improve my code? Thank you in advance.




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