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Equation 36 · Part 6 · A Reference Frame Becomes Classical by Publishing Its Orientation

fraction

d(R1,R2)=cos⁡−1 ⁣(Tr⁡(R1TR2)−12),d(R_1,R_2)= \cos^{-1}\!\left(\frac{\operatorname{Tr}(R_1^{\mathsf T}R_2)-1}{2}\right),
fraction

What this part means

Divide the expression above the line by the one below it.

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

The passage around this formula

For SO(3) , a coordinate-free angular distance between two rotations can be defined by d(R1,R2)=cos⁡−1 ⁣(Tr⁡(R1TR2)−12)d(R_1,R_2)= \cos^{-1}\!\left(\frac{\operatorname{Tr}(R_1^{\mathsf T}R_2)-1}{2}\right). with values from zero to π\pi . Radians are dimensionless in SI, but d still has the operational meaning of an angular error. A different group requires a declared invariant metric appropriate to that group. A coordinate chart’s Euclidean distance is not an acceptable substitute near its singularities.

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the article section

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