a1={0,-1/4,0}
a2={0,3/4,0}
a3={-1,1/4,0}
a4={1,1/4,0}
IdentityMatrix[3]a1.a1-Outer[Times,a1,a1]+IdentityMatrix[3]a2.a2-Outer[Times,a2,a2]+
IdentityMatrix[3]a3.a3-Outer[Times,a3,a3]+IdentityMatrix[3]a4.a4-Outer[Times,a4,a4]+{{1/3,0,0},{0,1/3,0},{0,0,2/3}}

          13             7             41
Out[8]= {{--, 0, 0}, {0, -, 0}, {0, 0, --}}
          12             3             12

{I1,I2,I3}=Diagonal[%]

solution=NDSolve[{w1'[t]==(I2-I3)/I1 w2[t] w3[t],
w2'[t]==(I3-I1)/I2 w1[t] w3[t],
w3'[t]==(I1-I2)/I3 w2[t] w1[t],
w1[0]==.001,
w2[0]==10,
w3[0]==0},
{w1,w2,w3},{t,0,10}]

Plot[Evaluate[w2[t] /. solution],{t,0,10}]
Plot[Evaluate[w1[t] /. solution],{t,0,10}]
Plot[Evaluate[w3[t] /. solution],{t,0,10},PlotRange->All]


solution=NDSolve[{w1'[t]==(I2-I3)/I1 w2[t] w3[t],
w2'[t]==(I3-I1)/I2 w1[t] w3[t],
w3'[t]==(I1-I2)/I3 w2[t] w1[t],
w2[0]==.1,
w1[0]==10,
w3[0]==0},
{w1,w2,w3},{t,0,10}]

ParametricPlot[Evaluate[{w2[t],w3[t]} /. solution],{t,0,10}]
Plot[Evaluate[w2[t] /. solution],{t,0,10}]
Plot[Evaluate[w1[t] /. solution],{t,0,10}]
Plot[Evaluate[w3[t] /. solution],{t,0,10},PlotRange->All]

