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Equation 36 · Part 1 · A Reference Frame Becomes Classical by Publishing Its Orientation

Symbol d

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),
dd

What this part means

d is part of the quantity the equation computes from the expression on the right.

Its job in the formula

d is part of the quantity the equation computes from the expression on the right.

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 function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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