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发帖数: 3022 | 1 X_i(t) = R_{ij}(t) Y_j
R_{ij}(t) is an orthogonal matrix, Y_j a constant vector.
Now,
dX_i(t)/dt = dR_{ij}(t)/dt Y_j = dR_{ij}(t)/dt R_{lj} R_{lm} Y_m
= dR_{ij}(t)/dt R_{lj} X_l
just need to show that dR_{ij}/dt R_{lj} is antisymmetric, which is easy:
dR_{ij}/dt R_{lj} = d(R_{ij}R_{lj})/dt - R_{ij} dR_{lj}/dt = - R_{ij}
dR_{lj}/dt
Now you have
dX_i/dt = A_il X_l,
where A_il is antisymmetric. Since A_il is antisymmetric in 3D, there
exist \Omega_k (the |
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