- #1
Curl
- 758
- 0
Ok here is what I did:
[tex]
T=\int \vec{\tau} \cdot d\vec{\theta } = \int\frac{\mathrm{d} \vec{L}}{\mathrm{d} t}\cdot d\vec{\theta } = \int \vec{L}\cdot d\vec{\omega} = \int I_{ij}\vec{\omega}\cdot d\vec{\omega}[/tex]
Where I is the inertia matrix.
when I carry that out, I get:
T= 0.5*(I11wx2+I22wy2+I33wz2) + 2*(I12wxwy+I13wxwz+I23wzwy)
but the real answer has no factor of 2 in the second term. What's wrong?
[tex]
T=\int \vec{\tau} \cdot d\vec{\theta } = \int\frac{\mathrm{d} \vec{L}}{\mathrm{d} t}\cdot d\vec{\theta } = \int \vec{L}\cdot d\vec{\omega} = \int I_{ij}\vec{\omega}\cdot d\vec{\omega}[/tex]
Where I is the inertia matrix.
when I carry that out, I get:
T= 0.5*(I11wx2+I22wy2+I33wz2) + 2*(I12wxwy+I13wxwz+I23wzwy)
but the real answer has no factor of 2 in the second term. What's wrong?