❓In the linear tensor form, what is the explicit expression for the components of the tensor in terms

In the linear tensor form, what is the explicit expression for the components of the tensor in terms of mass and angular velocity?

The components of the tensor $T^{i j}$ are: $T^{i j}=m\left(\omega^i \omega^j-\omega^2 \delta^{i j}\right)$ , where $\delta^{i j}$ is the Kronecker delta and $\omega^2=\omega^k \omega^k$.

The expression $T^{i j}=m\left(\omega^i \omega^j-\omega^2 \delta^{i j}\right)$ is the centrifugal force tensor in component form. It is derived by rearranging the equation for the centrifugal force, $F_c^i=m\left[\omega^i\left(\omega^j x^j\right)-\omega^2 x^i\right]$, into the linear tensor product form, $F_c^i=T^{i j} x^j$.

This tensor $T^{i j}$ mathematically encodes how the centrifugal force depends on the mass and rotation parameters, allowing the force $F_c^i$ to be calculated simply by multiplying $T^{i j}$ by the position vector $x^j$.

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