quaternion In A Sentence
Learn how to use quaternion in a sentence and make better sentences with `quaternion` by reading quaternion sentence examples.
- Considering the target angle rate changing, an adaptive attitude tracking control law was designed based on the error quaternion, and the corresponding close system stability was also proved.
- In contrast, the quaternion conjugation can be expressed arithmetically:.
- There are two applications to the RB. One is array processing and the other is quaternion finite field transform.
- It is realized by real quaternion overrides the weakness of matrix such as unintuitionistic, complex calculation.
- "H " is closed under quaternion multiplication and addition, which makes it a subring of the ring of all quaternions "'H " '.
- Each ( proper ) rotation is represented by a quaternion with unit norm.
- Shaw, in America, independently of Joly, has interpreted the quaternion as a point-symbol.
- Replaces the current quaternion with its natural logarithm.
- And by it, we turn linear matrix equation over quaternion field into linear equations over a number field, and obtain normal solutions of this kind of equation.
- Some inequalities of eigenvalues for weak cycle products of self - conjugate quaternion matrices are given.
- Two control laws are presented for attitude regulation of a rigid body expressed by quaternion.
- The unit quaternion transformation and vector algebra are applied to be analysis tools.
- An attitude quaternion feedback control system directly consists of linear error-quaternion feedback and linear body-rates feedback.
- For concreteness, one can take, and then the Hopf fibration can be defined as the map sending a unit quaternion.
- A 2D harmonic model based on the quaternion was constructed, and a special four-order cumulant was defined. The 2D cubic nonlinear phase coupling of additive color Gaussian noises was analyzed.
- This interest also led to Feza's work on quaternion analyticity, which continued practically to the end of his life .".
- The outer and inner products of two extensive quantities A, B, are in many ways analogous to the quaternion symbols Vab and Sab respectively.
- That is, the components of the quaternion correspond to the scalar and bivector parts of the following expression:.
- The tensor of a quaternion is a tensor of order zero.
- The eight-vecter algebra is found in the paper, as a kind of square matrix algebra and as more complete operation system containing the complex number vecter algebra and quaternion numbers.
- These results further enrich and develop the quaternion matrix algebra and the theory of generalized inverses.
- Gauss-Newton error minimization is used to transform six-dimentional reference vector to quaternion as a part of observations for EKF, which significantly reduces the computational requirement.
- Slerp also has expressions in terms of quaternion algebra, all using exponentiation.
- These may be compared and contrasted with such quaternion formulae as S(VabVcd) =SadSbc-SacSbd dSabc = aSbcd - bScda+cSadb where a, b, c, d denote arbitrary vectors.
- So it remains an intriguing question, whether e.g. gage field theory is more naturally quantised using quaternion Hilbert space, H.
- Given a four dimensional vector, and pretending that it is a quaternion, we can rotate the vector like this:.
- The norm of a quaternion is similar to that of a vector.
- Quaternion arithmetic in practice.
- The right characteristic values of matrices on quaternion division algebra are discussed, and some corresponding results for complex matrices are generalized and improved.
- Of arithmetic expressions and assignment statements and generate semantic analysis of quaternion sequence.
- This quantity is nowadays called the norm of the quaternion ".
- We proved that each square quaternion matrix has at least one right characteristic principal value and its eigenvector, and a concrete solution was given.
- A quaternion can be used to represent any arbitrary rotation.
- Quaternion can avoid gibbs lock if you use euler angle to rotate 3 d model.
- MacFarlane was the secretary of the quaternion Society and compiler of its publications.
- Other quaternion properties can be similarly related to or derived from geometric algebra.
- Proof of the quaternion rotation identity.
- The stabilizer of 4 points is the quaternion group.
- The construction of arithmetic Kleinian groups from quaternion algebras gives rise to particularly interesting hyperbolic manifolds.
- Block diagrams illustrate the conversion of an airplane motion parameters from body to earth axis for Euler angles and for the quaternion parameters.
- So long as the base point,, is not the antipode,, the quaternion.
- In 1947 some elements of inversive quaternion geometry were described by P . G . Gormley in his paper " Stereographic projection and the linear fractional group of transformations of quaternions ".
- Hamilton seems never to have been quite satisfied with the apparent heterogeneity of a quaternion, depending as it does on a numerical and a directed part.
- There was even a professional research association, the quaternion Society, devoted to the study of quaternions and other hypercomplex number systems.
- Considered with the operations of component-wise addition, and multiplication according to the quaternion group, this collection forms a 4-dimensional unit or a zero divisor.
- A unit quaternion has m = 1. det( Q R)= m 4.
- Calculates the natural logarithm of a quaternion.
- The Latin term for " turn " is versor, which is a quaternion that can be visualized as an arc of a great circle.
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