For cube size 0.1,1,1, Mass=100; Initial angular velocity=ω(0)=[1;0.25;0.5]; we get

Moment of inertia tensor=I=[16.67,0,0;0,8.42,0;0,0,8.42]; Angular momentum magnitude=|L|=17.32;

If body axes=x’,y’,z’;

θ(t)=θ(0)=acos(I1ω1/|L|)=0.27; [rad; x’ with respect to L]

ϕ(t)=t*|L|/I3=2.05*t; [rad; x’ rotation about L]

Ψ(t)=tω1(I3-I1)/I3=-0.97t; [rad; z’ rotation about x’]

1)What’s the meaning of the negative(-0.97), is it mean that z’ has left-handed rotation about x’?

2)x’ preccess about L every 3.06s; and z’ rotate about x’ every -6.47s; But if we use the simulation in the link and draw z’, we see that after 6s z’ complete more than 1 circle about x’, why? It should do so only after 6.47s doesn’t it?

simulation link: http://www.ialms.net/sim/3d-rigid-body-simulation/

For cube size 0.1,1,1, Mass=100; Initial angular velocity=ω(0)=[1;0.25;0.5]; we get

Moment of inertia tensor=I=[16.67,0,0;0,8.42,0;0,0,8.42]; Angular momentum magnitude=|L|=17.32;

If body axes=x’,y’,z’;

θ(t)=θ(0)=acos(I1ω1/|L|)=0.27; [rad; x’ with respect to L]

ϕ(t)=t*|L|/I3=2.05*t; [rad; x’ rotation about L]

Ψ(t)=tω1(I3-I1)/I3=-0.97t; [rad; z’ rotation about x’]

1)What’s the meaning of the negative(-0.97), is it mean that z’ has left-handed rotation about x’?

2)x’ preccess about L every 3.06s; and z’ rotate about x’ every -6.41s; But if we use the simulation in the link and draw z’, we see that after 6s z’ complete more than 1 circle about x’, why? It should do so only after 6.41s doesn’t it?

simulation link: http://www.ialms.net/sim/3d-rigid-body-simulation/

For cube size 0.1,1,1, Mass=100; Initial angular velocity=ω(0)=[1;0.25;0.5]; we get

Moment of inertia tensor=I=[16.67,0,0;0,8.42,0;0,0,8.42]; Angular momentum magnitude=|L|=17.32;

If body axes=x’,y’,z’;

θ(t)=θ(0)=acos(I1ω1/|L|)=0.27; [rad; x’ with respect to L]

ϕ(t)=t*|L|/I3=2.05*t; [rad; x’ rotation about L]

Ψ(t)=tω1(I3-I1)/I3=-0.97t; [rad; z’ rotation about x’]

1)What’s the meaning of the negative(-0.97), is it mean that z’ has left-handed rotation about x’?

2)x’ preccess about L every 3.06s; and z’ rotate about x’ every -6.47s; But if we use the simulation in the link and draw z’, we see that after 6s z’ complete more than 1 circle about x’, why? It should do so only after 6.47s doesn’t it?

simulation link: http://www.ialms.net/sim/3d-rigid-body-simulation/

For cube size 0.1,1,1, Mass=100; Initial angular velocity=ω(0)=[1;0.25;0.5]; we get

Moment of inertia tensor=I=[16.67,0,0;0,8.42,0;0,0,8.42]; Angular momentum magnitude=|L|=17.32;

If body axes=x’,y’,z’;

θ(t)=θ(0)=acos(I1ω1/|L|)=0.27; [rad; x’ with respect to L]

ϕ(t)=t*|L|/I3=2.05*t; [rad; x’ rotation about L]

Ψ(t)=tω1(I3-I1)/I3=-0.97t; [rad; z’ rotation about x’]

1)What’s the meaning of the negative(-0.97), is it mean that z’ has left-handed rotation about x’?

2)x’ preccess about L every 3.06s; and z’ rotate about x’ every -6.47s; But if we use the simulation in the link and draw z’, we see that after 6s z’ complete more than 1 circle about x’, why? It should do so only after 6.47s doesn’t it?

simulation link: http://www.ialms.net/sim/3d-rigid-body-simulation/