Euler's rotation theorem states that any rotation in three-dimensional space can be described as a single rotation about a fixed axis. This theorem implies that the orientation of a rigid body can be represented using an axis-angle representation, simplifying the understanding of rotational dynamics.

Euler's Rotation Theorem

Euler's rotation theorem

rotation in three-dimensional space

single rotation about a fixed axis

orientation of a rigid body

Axis-Angle Representation is a mathematical model used to describe the orientation of a rigid body in three-dimensional space, where a rotation is defined by an axis of rotation and an angle of rotation around that axis. This representation is particularly useful in robotics and computer graphics for interpolating rotations and converting between different rotation representations like quaternions and rotation matrices.

axis-angle representation

Rotational dynamics is the branch of physics that deals with the motion of objects that rotate around an axis, involving the study of torques and angular momentum. It helps explain phenomena ranging from the spin of a figure skater to the rotation of celestial bodies, providing a comprehensive understanding of rotational motion and its effects.

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