📢Transformation of the Rotating Polar Tensor Basis to Cartesian Coordinates

The analysis demonstrates that unlike the fixed Cartesian basis vectors, the polar basis vectors are dynamic and change direction with the angle. The explicit transformation of the polar tensor basis into the fixed Cartesian tensor basis, achieved by taking the outer product of the polar basis vectors, revealing that each of the four polar basis tensors is a linear combination of the Cartesian tensors. The coefficients of these combinations are directly dependent on trigonometric functions of the angle, which visually and mathematically confirms that the polar tensor basis rotates with its corresponding coordinate system.

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