hodograph

简明释义

英[ˈhoʊdəˌgræf]美[ˈhoʊdəˌgræf]

n. 速度图；速矢端线；[物] 矢端曲线

英英释义

单词用法

同义词

反义词

例句

1.These two airfoils lie on different Riemann sheets in the hodograph plane.

该两个翼型处在不同的黎曼面内。

2.Peak updraft strength is slightly enhanced with hodograph curvature.

山顶上升气流强度随速矢端迹曲率加大而稍有加强。

3.From 3-component record one can see in noise-free single signal circumstances, the hodograph distribution of linear polarization wave should present itself as a straight line.

反映在三分量记录上，在没有噪音的单一信号情况下，线性极化波的矢端分布应该是一条直线。

4.This paper deals with the inverse design problem of transonic turbine cascade in the hodograph plane by the finite area method.

本文给出了基于有限面积法的跨音速透平叶栅速度面反问题设计方法。

5.A transformation that is most useful in the application of the hodograph method is the inversion transformation.

在速端曲线法的应用中，一种最有用的变换是反演变换。

6.From 3-component record one can see in noise-free single signal circumstances, the hodograph distribution of linear polarization wave should present itself as a straight line.

反映在三分量记录上，在没有噪音的单一信号情况下，线性极化波的矢端分布应该是一条直线。

7.A circular hodograph 速度图 indicates uniform wind speed at all levels.

圆形的 hodograph 速度图 表示各个高度的风速均匀。

8.By analyzing the hodograph 速度图, researchers can determine the stability of the atmosphere.

通过分析 hodograph 速度图，研究人员可以确定大气的稳定性。

9.In meteorology, the hodograph 速度图 is used to visualize wind speed and direction at various altitudes.

在气象学中，hodograph 速度图 用于可视化不同高度的风速和方向。

10.The hodograph 速度图 can help meteorologists predict severe weather patterns.

hodograph 速度图 可以帮助气象学家预测严重的天气模式。

11.The slope of the hodograph 速度图 can indicate changes in wind shear.

在 hodograph 速度图 中，斜率可以指示风切变的变化。

作文

In the realm of mathematics and physics, particularly in the study of motion, the term hodograph refers to a geometric representation of the velocity of a moving object. This concept is not only fascinating but also essential for understanding the dynamics of various physical systems. A hodograph can be defined as a curve traced out by the tip of a vector representing the velocity of an object over time. Essentially, it provides a visual way to analyze how an object's speed and direction change as it moves through space.To grasp the significance of a hodograph, consider the motion of a car driving along a winding road. As the car accelerates, decelerates, and changes direction, its velocity vector constantly varies. By plotting these velocity vectors at different points in time, we can create a hodograph that captures the essence of the car's motion. This allows us to better understand the relationship between speed, direction, and the forces acting on the vehicle.One of the most intriguing aspects of hodographs is their ability to simplify complex problems in physics. For instance, when dealing with projectile motion, the hodograph can help us visualize the trajectory of the object in a more manageable way. Instead of focusing solely on the object's position, we can analyze its velocity and acceleration, leading to deeper insights into the underlying mechanics.Moreover, hodographs are not limited to classical mechanics; they also find applications in other fields such as engineering, aerodynamics, and even economics. In engineering, for example, understanding the velocity of fluid flow can be crucial for designing efficient systems. By utilizing hodographs, engineers can predict how fluids will behave under various conditions, ultimately leading to more effective designs and solutions.In aerodynamics, the concept of hodographs plays a critical role in analyzing the performance of aircraft. By examining the velocity vectors of an airplane during flight, engineers can optimize its design for better fuel efficiency and stability. This application highlights how the theoretical aspects of hodographs translate into practical benefits in real-world scenarios.Furthermore, the mathematical foundation of hodographs is rooted in vector calculus and differential equations. Understanding how to derive and manipulate these equations is essential for anyone looking to delve deeper into the field of physics or engineering. The ability to visualize motion through hodographs not only enhances our comprehension of these subjects but also fosters critical thinking and problem-solving skills.In conclusion, the concept of hodograph serves as a powerful tool for analyzing motion in various fields of study. Its ability to represent velocity visually simplifies complex problems and provides valuable insights into the behavior of moving objects. Whether in physics, engineering, or other disciplines, mastering the use of hodographs can lead to a greater understanding of the principles governing motion and ultimately contribute to advancements in technology and science. As we continue to explore the intricacies of motion, the hodograph will undoubtedly remain a vital component of our analytical toolkit.

在数学和物理的领域，特别是在运动研究中，术语hodograph指的是一个运动物体速度的几何表示。这个概念不仅令人着迷，而且对于理解各种物理系统的动态至关重要。hodograph可以定义为一个曲线，该曲线由表示物体随时间变化的速度的向量的尖端所描绘。基本上，它提供了一种可视化的方法来分析物体在空间中移动时速度和方向如何变化。为了更好地理解hodograph的重要性，考虑一下一辆车沿着蜿蜒道路行驶的运动。当汽车加速、减速并改变方向时，其速度向量不断变化。通过在不同时间点绘制这些速度向量，我们可以创建一个hodograph，捕捉汽车运动的本质。这使我们能够更好地理解速度、方向和作用于车辆的力之间的关系。hodograph最令人着迷的方面之一是它们能够简化物理学中的复杂问题。例如，在处理抛体运动时，hodograph可以帮助我们以更可管理的方式可视化物体的轨迹。我们不仅关注物体的位置，还可以分析其速度和加速度，从而对潜在的力学原理获得更深入的见解。此外，hodograph并不限于经典力学；它们还在工程学、空气动力学甚至经济学等其他领域找到了应用。在工程学中，了解流体流动的速度对于设计高效的系统至关重要。通过利用hodographs，工程师可以预测流体在各种条件下的行为，最终导致更有效的设计和解决方案。在空气动力学中，hodograph的概念在分析飞机性能中起着关键作用。通过检查飞机在飞行过程中的速度向量，工程师可以优化其设计，以提高燃油效率和稳定性。这个应用突显了hodograph的理论方面如何转化为现实场景中的实际利益。此外，hodograph的数学基础植根于向量微积分和微分方程。理解如何推导和操作这些方程对于任何希望深入物理或工程领域的人来说都是必不可少的。通过hodographs可视化运动，不仅增强了我们对这些学科的理解，还培养了批判性思维和解决问题的能力。总之，hodograph的概念作为分析各种研究领域中运动的强大工具。它以可视化方式表示速度，简化了复杂问题，并提供了对运动物体行为的宝贵见解。无论是在物理学、工程学还是其他学科，掌握hodographs的使用都可以导致对运动规律的更大理解，并最终有助于技术和科学的进步。随着我们继续探索运动的复杂性，hodograph无疑将继续成为我们分析工具箱中的重要组成部分。