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Matrix wizard

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
  • Choose extrinsic composition and the rotation sign convention

    0 0 0
    0 0 0
    0 0 0
    0 0 0
    0 0 0
    0 0 0
    0 0 0
    0 0 0
    0 0 0

    Press to see the result of the product

    1 2 3
    4 5 0
    0 0 0

    0 0 0
    0 0 0
    0 0 0

    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
  • Choose the ordered rotations for the intrinsic composition and the rotation sign convention

    0 0 0
    0 0 0
    0 0 0
    0 0 0
    0 0 0
    0 0 0
    0 0 0
    0 0 0
    0 0 0

    Press to see the result of the product

    0 0 0
    0 0 0
    0 0 0

    0 0 0
    0 0 0
    0 0 0

    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


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