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Statements

Subject Item
dbr:Three-dimensional_rotation_operator
rdfs:label
Three-dimensional rotation operator
rdfs:comment
This article derives the main properties of rotations in 3-dimensional space. The three Euler rotations are one way to bring a rigid body to any desired orientation by sequentially making rotations about axis' fixed relative to the object. However, this can also be achieved with one single rotation (Euler's rotation theorem). Using the concepts of linear algebra it is shown how this single rotation can be performed.
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dbc:Kinematics dbc:Linear_algebra dbc:Rotation_in_three_dimensions
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18676962
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1069705586
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dbr:Euclidean_vector dbr:Euler_angles dbr:Rodrigues'_rotation_formula dbr:Coordinate_system dbc:Kinematics dbr:Rotation_(mathematics) dbr:Characteristic_polynomial dbr:Linear_operator dbc:Linear_algebra dbr:Rotations dbr:Cross_product dbr:3-dimensional_space dbr:Hodge_star dbr:Operator_(mathematics) dbr:Eigenspace dbr:Eigenvalue dbr:Rigid_body dbc:Rotation_in_three_dimensions dbr:Euler's_rotation_theorem dbr:Determinant dbr:Matrix_(mathematics) dbr:Orthogonal_matrix dbr:Identity_matrix dbr:Euler_angle dbr:Linear_algebra
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This article derives the main properties of rotations in 3-dimensional space. The three Euler rotations are one way to bring a rigid body to any desired orientation by sequentially making rotations about axis' fixed relative to the object. However, this can also be achieved with one single rotation (Euler's rotation theorem). Using the concepts of linear algebra it is shown how this single rotation can be performed.
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