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相关概念视频

Velocity and Position by Graphical Method01:34

Velocity and Position by Graphical Method

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Velocity and position can be calculated from the known function of acceleration as a function of time. The total area under the acceleration-time graph and the velocity-time graph gives the change in velocity and position, respectively. In the case of an airplane, its acceleration is tracked using the inertial navigation system. The pilot provides the input of the airplane's initial position and velocity before takeoff. The inertial navigation system then uses the acceleration data to...
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Average and Instantaneous Velocity Vectors01:12

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To calculate other physical quantities in kinematics, the time variable must be introduced. The time variable not only allows us to state where an object is (its position) during its motion, but also how fast it’s moving. The speed at which an object is moving is given by the rate at which the position changes with time. For each position, a particular time is assigned. If the details of the motion at each instant are not important, the rate is usually expressed as the average velocity v.
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Average Velocity01:12

Average Velocity

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To calculate the other physical quantities in kinematics, we must introduce the time variable. The time variable allows us not only to state the position of the object during its motion, but also how fast it is moving. The speed at which an object is moving is given by the rate at which the position changes with time. For each position xi, we assign a particular time ti. If the details of the motion at each instant are not important, the rate is usually expressed as the average velocity. This...
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Position and Displacement01:31

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The position of an object defines its location relative to a convenient frame of reference at any particular time. A frame of reference is an arbitrary set of axes from which the position and motion of an object are described. Earth is often used as a frame of reference, and we often describe the position of an object as it relates to stationary objects on Earth. For example, a rocket launch could be described in terms of the position of the rocket with respect to Earth as a whole. On the other...
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Area Computation by the Alternative Coordinate Method01:24

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The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...
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Position and Displacement Vectors01:00

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To describe the motion of an object, one should first be able to describe its position (where it is at any particular time). More precisely, the position needs to be specified relative to a convenient frame of reference. A frame of reference is an arbitrary set of axes from which the position and motion of an object are described. Earth is often used as a frame of reference to describe the position of an object in relation to stationary objects on Earth.
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关于计算空间移位平均值的计算.

Q J Ge1, Zihan Yu1, Mona Arbab2

  • 1Computational Design Kinematics Lab, Stony Brook University, SUNY, Stony Brook, New York, 11794-2300.

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PubMed
概括
此摘要是机器生成的。

这项研究引入了一种新的双四边形动力测量方法,用于平均空间位移,比传统方法 (如欧勒角度和生物力学和医学成像中的单元四边形) 更准确.

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科学领域:

  • 生物力学 生物力学
  • 医疗成像医学成像
  • 机器人技术 机器人技术 机器人技术
  • 计算机视觉 计算机视觉

背景情况:

  • 动力学错误分析在生物力学和医学成像学中对于统计患者组分析至关重要.
  • 使用欧勒角或单位四次数来平均空间位移的现有方法具有局限性,包括与单位四次数的潜在标志模糊性问题.

研究的目的:

  • 研究和比较计算从一组给定位移的平均空间位移的方法.
  • 引入和验证基于双四次子的新型动力学测量方法,以提高平均空间位移的准确性.
  • 为了解决现有的参数表示的局限性,如欧勒角和单位四次数.

主要方法:

  • 使用欧勒角和转换向量,单元四次元和转换向量以及双四次元的平均算法的比较.
  • 使用一种新的双四边形动力测量方法,制定一个受约束最小平方最小化问题.
  • 将问题分解为转换向量的独立优化 (中心) 和单元四次数 (自身向量分析).

主要成果:

  • 双四边形方法为平均空间位移提供了一个强大的方法,克服了单位四边形方法中存在的符号模两可的问题.
  • 最佳转换向量是输入转换向量的中心点.
  • 最优单元四次子是由对应于特定矩阵的最小自值的自向量得出的,独立于权重因子.
  • 比例表明,与其他方法相比,双四子方法的有效性和准确性得到了提高.

结论:

  • 双四边子为在需要高动力学精度的应用中平均空间位移提供了优越的框架.
  • 拟议的双四边形方法在计算上是高效的,并且避免了与其他表示相关的常见陷.
  • 这项工作为生物力学和医学成像等领域的动力学数据的统计分析提供了宝贵的工具.