1. Replaces the current quaternion with its natural logarithm.

2. Calculates the natural logarithm of a quaternion.

3. In this paper, we firstly consider a quaternion algebra.

4. These results further enrich and develop the quaternion matrix algebra. The dissertation is divided into 5 chapters.

5. Quaternion can avoid gibbs lock if you use euler angle to rotate 3 d model.

6. 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.

7. This paper contains two parts:1. Algebraic operations of quaternion are defined by utilizing the knowledge in vector algebra and the fundamental properties of algebra of quaternions are derived.

8. A quaternion can be used to represent any arbitrary rotation.

9. It is realized by real quaternion overrides the weakness of matrix such as unintuitionistic, complex calculation.

10. It"s proved that the algorithm optimization of quaternion raise the precision and the calculate efficiency. 2."

11. The norm of a quaternion is similar to that of a vector.

12. Quaternion definition and geometry meaning were described and quaternion movement equation was introduced.

13. And also develop the quaternion algorithm error equation using calculated value of the predictor and corrector stage of attitude algorithm.

14. We proved that each square quaternion matrix has at least one right characteristic principal value and its eigenvector, and a concrete solution was given.

15. All the existing Methods : Utilize quaternion algebra to iteratively compute M - sets'boundaries.

16. Two control laws are presented for attitude regulation of a rigid body expressed by quaternion.

17. A class of linear sliding manifolds is selected in terms of the error quaternion. Based on a Lyapunov function candidate,[sentencedict .com] the SMC algorithm is derived.

18. Some inequalities of eigenvalues for weak cycle products of self - conjugate quaternion matrices are given.

19. There are two applications to the RB. One is array processing and the other is quaternion finite field transform.

20. In the paper the generalized numerical radiuses of real quaternion matrices with symmetric function are defined and theirs inequalities are given.

21. Eight , design SAMPLE language grammar, semantic analyzer, the output quaternion type of intermediate results.

22. The road initial profile is gotten by marked watershed segmentation in quaternion space with multi-spectral images which solve the question of how to set the initial border in the model.

23. The method of adjusting screen - coordinate and object - coordinate of plane model with quaternion is discussed.

24. In this system, MEMS–gyroscopes are adopted to sense the angular rate, quaternion method is adopted to get the altitude of vision table and step motors are adopted as drivers.

25. Finally, the 3-D M-sets generated by the ternary number and quaternion algebra are both rendered by our new algorithm.

26. Of arithmetic expressions and assignment statements and generate semantic analysis of quaternion sequence.

27. 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.

28. The mathematical deduction and confirmation of the algorithm are introduced in the paper, which is a powerfully effective one for solving the quaternion matrix differential equation.

29. In this paper, we obtain some inequalities for norm and traces of quaternion matrices.

30. The third phase of the form of intermediate code using easy - to - read type Quaternion.

31. The right characteristic values of matrices on quaternion division algebra are discussed, and some corresponding results for complex matrices are generalized and improved.

32. Introduce the principium and method of Euler angle algorithm, direction cosine algorithm, Quaternion algorithm, and Rotation Vector algorithm.

33. The unit quaternion transformation and vector algebra are applied to be analysis tools.

34. These results further enrich and develop the quaternion matrix algebra and the theory of generalized inverses.

35. Two control laws are presented for attitude regulation of a rigid body expressed by unit quaternion.

36. 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.

37. 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.

38. A OpenGL program to demonstrate using Quaternion to rotate 3 d model.

39. An attitude quaternion feedback control system directly consists of linear error-quaternion feedback and linear body-rates feedback.

40. First, according to the tracking error dynamics and kinematics described by unit quaternion error and angular velocity error, a sliding mode controller is derived based on Lyapunov theory.

41. The cooperative control law for multiple rigid body systems is designed. Numerical results show the attitude quaternion of every rigid body can be controlled to convergently approach its stable value.

42. 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.

43. This paper introduces the principle of fiber optic gyro, studies the attitude algorithm of fiber optic gyro ship attitude system, introduces the quaternion algorithm and rotation vector algorithm.

44. The main purpose of this paper is to study a new proof of extended unitary diagonalizable of self-conjugate matrix in quaternion field and deduce other properties concerned.

45. Thetheory includes Euler angular algorithm, direction cosine algorithm, quaternion algorithm and rotation vector algorithm.