Generate matrix as extrinsic rotations composition
When the three rotations are applied over the reference frame axes, for example in order z-x-z, it is equivalent to a right-product of matrices
The first rotation moves the body around the external 'z' axis an angle φ
The second rotation moves the body around the external 'x' axis an angle θ
The third rotation moves the body again around the external 'z' axis an angle ψ
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Press to see the result of the product
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The notation has been made short by using the order that composition implies (1 for φ, 2 for θ and 3 for ψ) and writing sK and cK for sin and cos of the K-th angle
Generate a matrix as composition of intrinsic rotations
When the three rotations are applied over the moving body axes, for example in order Z-X-Z, it is equivalent to a right-product of matrices
The first rotation moves the body around its axis Z an angle with value ψ
The second rotation moves the body around its axis X an angle θ
The third rotation moves the body around its axis Z again an angle with value φ
After this three rotations:
ψ will be the external angle of the static construction
θ will be the medium angle of the static construction
φ will be the internal angle of the static construction
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Press to see the result of the product
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The notation has been made short by using the order that composition implies (1 for ψ, 2 for θ and 3 for φ) and writing sK and cK for sin and cos of the K-th angle
