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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.
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:
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 ...
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 ...
Quaternionic analysis. In mathematics, quaternionic analysis is the study of functions with quaternions as the domain and/or range. Such functions can be called functions of a quaternion variable just as functions of a real variable or a complex variable are called. As with complex and real analysis, it is possible to study the concepts of ...
The utricle and saccule are the two otolith organs in the vertebrate inner ear. The word utricle comes from Latin uter 'leather bag'. The utricle and saccule are part of the balancing system (membranous labyrinth) in the vestibule of the bony labyrinth (small oval chamber). [1] They use small stones and a viscous fluid to stimulate hair cells ...
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 mathematical field of representation theory, a quaternionic representation is a representation on a complex vector space V with an invariant quaternionic structure, i.e., an antilinear equivariant map. which satisfies. Together with the imaginary unit i and the antilinear map k := ij, j equips V with the structure of a quaternionic vector ...