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In mathematics, the dual quaternions are a … In mathematics, the dual quaternions are an 8-dimensional real algebra isomorphic to the tensor product of the quaternions and the dual numbers. Thus, they may be constructed in the same way as the quaternions, except using dual numbers instead of real numbers as coefficients. A dual quaternion can be represented in the form A + εB, where A and B are ordinary quaternions and ε is the dual unit, which satisfies ε2 = 0 and commutes with every element of the algebra. Unlike quaternions, the dual quaternions do not form a division algebra. In mechanics, the dual quaternions are applied as a number system to represent rigid transformations in three dimensions. Since the space of dual quaternions is 8-dimensional and a rigid transformation has six real degrees of freedom, three for translations and three for rotations, dual quaternions obeying two algebraic constraints are used in this application. Similar to the way that rotations in 3d space can be represented by quaternions of unit length, rigid motions in 3d space can be represented by dual quaternions of unit length. This fact is used in theoretical kinematics (see McCarthy), and in applications to 3D computer graphics, robotics and computer vision.er graphics, robotics and computer vision.
, En matemáticas, los cuaterniones duales co … En matemáticas, los cuaterniones duales constituyen un álgebra isomorfa al álgebra de Clifford de una forma cuadrática degenerada. En teoría de anillos, los cuaterniones duales son anillos construidos de la misma manera que los cuaterniones, excepto porque usan números duales en lugar de números reales como coeficientes. Un cuaternión dual puede representarse en la forma p + ε q, donde p y q son cuaterniones ordinarios y ε es la unidad dual (que satisface que εε = 0) y conmuta con cada elemento del álgebra. A diferencia de los cuaterniones, no forman un anillo de división. En mecánica, los cuaterniones duales se aplican como números para representar en tres dimensiones. Un cuaternión dual es un par ordenado de cuaterniones  = (A, B), construido a partir de ocho parámetros reales. Debido a que las transformaciones rígidas tienen seis grados reales de libertad, los cuaterniones dobles incluyen dos restricciones algebraicas para esta aplicación. De manera similar a la forma en que las rotaciones en el espacio 3D pueden representarse por cuaterniones de longitud unitaria, los movimientos rígidos en el espacio 3D pueden representarse por cuaterniones duales de longitud unitaria. Este hecho se usa en cinemática teórica (véase McCarthy), y en aplicaciones a 3D de computación gráfica, robótica y visión artificial.ón gráfica, robótica y visión artificial.
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En matemáticas, los cuaterniones duales co … En matemáticas, los cuaterniones duales constituyen un álgebra isomorfa al álgebra de Clifford de una forma cuadrática degenerada. En teoría de anillos, los cuaterniones duales son anillos construidos de la misma manera que los cuaterniones, excepto porque usan números duales en lugar de números reales como coeficientes. Un cuaternión dual puede representarse en la forma p + ε q, donde p y q son cuaterniones ordinarios y ε es la unidad dual (que satisface que εε = 0) y conmuta con cada elemento del álgebra. A diferencia de los cuaterniones, no forman un anillo de división.erniones, no forman un anillo de división.
, In mathematics, the dual quaternions are a … In mathematics, the dual quaternions are an 8-dimensional real algebra isomorphic to the tensor product of the quaternions and the dual numbers. Thus, they may be constructed in the same way as the quaternions, except using dual numbers instead of real numbers as coefficients. A dual quaternion can be represented in the form A + εB, where A and B are ordinary quaternions and ε is the dual unit, which satisfies ε2 = 0 and commutes with every element of the algebra. Unlike quaternions, the dual quaternions do not form a division algebra.uaternions do not form a division algebra.
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Cuaternión dual
, Dual quaternion
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