quaternion

简明释义

英[kwəˈtɜːnɪən]美[kwəˈtɜːrnɪən]

n. 四元数；四个一组；四人一组

英英释义

单词用法

同义词

反义词

例句

1.The sample and static error compensation, quaternion and attitude updating and algorithm of station and velocity updating were researched.

研究了采样与静差补偿，以及四元数、姿态、位置和速度更新的算法。

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

本文获得了四元数矩阵的范数和迹的一些不等式，改进了近期的某些结果。

3.Replaces the current quaternion with its natural logarithm.

用当前四元数的自然对数替换此四元数。

4.So, dual Euler method is better than quaternion method in the solution of the singularity of the Euler equation.

因此，对于解决欧拉方程奇异性来讲，双欧法要优于四元数法。

5.In this paper, decomposition of a quaternion matrix is systemically studied.

本文系统的研究了四元数矩阵分解理论。

6.Accordingly, we extended several important theorems of complex matrix theory to the quaternion field.

由此，把复数域上矩阵论的若干重要定理推广到了四元数体。

7.When working with 3D rotations, you may prefer a quaternion 四元数 over Euler angles to avoid gimbal lock.

在处理3D旋转时，你可能会选择 quaternion 四元数 而不是欧拉角以避免万向节锁定。

8.In computer graphics, a quaternion 四元数 is often used to represent rotations.

在计算机图形学中，quaternion 四元数 通常用于表示旋转。

9.A quaternion 四元数 consists of one real part and three imaginary parts.

一个 quaternion 四元数 由一个实部和三个虚部组成。

10.The physics engine uses a quaternion 四元数 to smoothly interpolate between orientations.

物理引擎使用 quaternion 四元数 来平滑地插值不同的方向。

11.In robotics, quaternions 四元数 are used to represent the orientation of robotic arms.

在机器人技术中，quaternion 四元数 用于表示机械臂的方向。

作文

In the realm of mathematics and physics, the concept of a quaternion is both fascinating and complex. A quaternion is a number system that extends the traditional notion of complex numbers. It is represented in the form of a four-dimensional vector, which consists of one real part and three imaginary parts. This unique structure allows quaternions to efficiently represent rotations in three-dimensional space, making them invaluable in various fields such as computer graphics, robotics, and aerospace engineering.The history of quaternions dates back to the mid-19th century when the Irish mathematician William Rowan Hamilton introduced this concept. He was searching for a way to extend complex numbers to higher dimensions, and his discovery laid the foundation for what we now understand as quaternions. Hamilton famously defined a quaternion as a mathematical entity that can be expressed as:q = a + bi + cj + dk,where 'a' is the real part, and 'b', 'c', and 'd' are the coefficients of the imaginary units 'i', 'j', and 'k'. These units follow specific multiplication rules that differ from those of traditional algebra, particularly because they do not commute. For example, ij = k, but ji = -k. This non-commutative property is one of the reasons why quaternions are so powerful in representing three-dimensional rotations.One of the primary advantages of using quaternions over other representations, such as Euler angles or rotation matrices, is their ability to avoid gimbal lock. Gimbal lock occurs when two of the three rotational axes align, causing a loss of one degree of freedom in the rotation representation. Quaternions provide a smooth and continuous representation of rotations, allowing for more efficient interpolation between orientations, which is particularly useful in animation and simulations.In computer graphics, quaternions play a crucial role in 3D modeling and animation. They enable developers to smoothly rotate objects without the complications associated with other methods. For instance, when animating a character in a video game, using quaternions allows for fluid movements and transitions, enhancing the overall visual experience. Additionally, quaternions require less computational power than rotation matrices, making them more efficient for real-time applications.Robotics is another field where quaternions have made significant contributions. In robotic motion planning and control, quaternions are used to represent the orientation of robots and their end effectors. This representation allows for precise calculations of movements and orientations, which are essential for tasks such as grasping objects or navigating through environments.In conclusion, the quaternion is a powerful mathematical tool that extends our understanding of rotations in three-dimensional space. Its unique properties make it indispensable in various fields, including computer graphics, robotics, and aerospace engineering. As technology continues to advance, the applications of quaternions will likely expand, further demonstrating their importance in modern science and engineering. Understanding quaternions not only enriches our knowledge of mathematics but also equips us with the tools needed to tackle complex problems in the real world.

在数学和物理的领域中，四元数的概念既迷人又复杂。四元数是一种扩展传统复数概念的数字系统。它以四维向量的形式表示，由一个实部和三个虚部组成。这种独特的结构使得四元数能够有效地表示三维空间中的旋转，使其在计算机图形学、机器人技术和航空航天工程等多个领域中不可或缺。四元数的历史可以追溯到19世纪中叶，当时爱尔兰数学家威廉·罗文·哈密顿提出了这一概念。他正在寻找一种将复数扩展到更高维度的方法，他的发现奠定了我们现在理解的四元数的基础。哈密顿著名地将四元数定义为：q = a + bi + cj + dk，其中'a'是实部，而'b'、'c'和'd'是虚单位'i'、'j'和'k'的系数。这些单位遵循特定的乘法规则，与传统代数不同，特别是因为它们不满足交换律。例如，ij = k，但ji = -k。这种非交换性是四元数在表示三维旋转时如此强大的原因之一。使用四元数而不是其他表示方法（如欧拉角或旋转矩阵）的主要优势之一是它们能够避免万向锁。万向锁发生在三个旋转轴中的两个对齐时，导致旋转表示中的一个自由度丧失。四元数提供了一种平滑和连续的旋转表示，允许在方向之间进行更高效的插值，这在动画和模拟中特别有用。在计算机图形学中，四元数在3D建模和动画中发挥了关键作用。它们使开发人员能够平滑地旋转对象，而不会遇到其他方法的复杂性。例如，在视频游戏中为角色动画时，使用四元数可以实现流畅的运动和过渡，从而增强整体视觉体验。此外，四元数所需的计算能力低于旋转矩阵，使其在实时应用中更为高效。机器人技术是另一个四元数做出重大贡献的领域。在机器人运动规划和控制中，四元数用于表示机器人的方向及其末端执行器。这种表示法允许对运动和方向进行精确计算，这对于抓取物体或在环境中导航等任务至关重要。总之，四元数是一种强大的数学工具，扩展了我们对三维空间中旋转的理解。其独特的性质使其在计算机图形学、机器人技术和航空航天工程等多个领域中不可或缺。随着技术的不断进步，四元数的应用可能会进一步扩展，进一步证明其在现代科学和工程中的重要性。理解四元数不仅丰富了我们对数学的知识，还为我们提供了解决现实世界复杂问题所需的工具。