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A spatial rotation around a fixed point of radians about a unit axis that denotes the Euler axis is given by the quaternion , where and . Compared to rotation matrices, quaternions are more compact, efficient, and numerically stable. Compared to Euler angles, they are simpler to compose.
t. e. Motion, the process of movement, is described using specific anatomical terms. Motion includes movement of organs, joints, limbs, and specific sections of the body. The terminology used describes this motion according to its direction relative to the anatomical position of the body parts involved. Anatomists and others use a unified set ...
Euler angles (in 3-2-1 sequence) to quaternion conversion. By combining the quaternion representations of the Euler rotations we get for the Body 3-2-1 sequence, where the airplane first does yaw (Body-Z) turn during taxiing onto the runway, then pitches (Body-Y) during take-off, and finally rolls (Body-X) in the air.
The vestibular system, in vertebrates, is a sensory system that creates the sense of balance and spatial orientation for the purpose of coordinating movement with balance. Together with the cochlea, a part of the auditory system, it constitutes the labyrinth of the inner ear in most mammals. As movements consist of rotations and translations ...
Classical elements of a quaternion. Hamilton defined a quaternion as the quotient of two directed lines in tri dimensional space; [1] or, more generally, as the quotient of two vectors. [2] A quaternion can be represented as the sum of a scalar and a vector. It can also be represented as the product of its tensor and its versor.
The set of quaternions is a 4-dimensional vector space over the real numbers, with as a basis, by the component-wise addition. and the component-wise scalar multiplication. A multiplicative group structure, called the Hamilton product, denoted by juxtaposition, can be defined on the quaternions in the following way:
The standard anatomical position, or standard anatomical model, is the scientifically agreed upon reference position for anatomical location terms. Standard anatomical positions are used to standardise the position of appendages of animals with respect to the main body of the organism. In medical disciplines, all references to a location on or ...
In mathematics, quaternions are a non-commutative number system that extends the complex numbers.Quaternions and their applications to rotations were first described in print by Olinde Rodrigues in all but name in 1840, [1] but independently discovered by Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space.