brachistochronic path

简明释义

最小时程;

英英释义

例句

1.The concept of a brachistochronic path can be applied in optimizing routes for delivery trucks.

最速路径的概念可以应用于优化送货卡车的路线。

2.In physics, finding the brachistochronic path helps us understand how objects move under the influence of gravity.

在物理学中，寻找最速路径帮助我们理解物体在重力影响下的运动方式。

3.The shortest time to travel between two points is along a brachistochronic path, which means it takes the least time compared to any other route.

在两点之间旅行的最短时间是沿着一条最速路径，这意味着它所需的时间比其他任何路线都要少。

4.Engineers often design roller coasters to follow a brachistochronic path for maximum thrill and speed.

工程师们通常设计过山车沿着最速路径行驶，以获得最大的刺激和速度。

5.Mathematicians study the brachistochronic path to solve complex problems related to calculus and motion.

数学家研究最速路径以解决与微积分和运动相关的复杂问题。

作文

In the world of physics and mathematics, the concept of a brachistochronic path plays a crucial role in understanding motion and optimization. The term 'brachistochrone' comes from the Greek words 'brachistos,' meaning shortest, and 'chronos,' meaning time. Therefore, a brachistochronic path refers to the path taken by an object that minimizes the time it takes to travel between two points under the influence of gravity. This fascinating problem was first posed by Johann Bernoulli in 1696 and has intrigued mathematicians and physicists ever since.To grasp the significance of a brachistochronic path, one must consider its application in real-world scenarios. Imagine a roller coaster that must transport riders from the top of a hill to the ground below. If the goal is to minimize the time spent traveling, the design of the track must follow a specific curve known as a cycloid. This curve is the solution to the brachistochrone problem, demonstrating how mathematical principles can be applied to engineering and design.The beauty of the brachistochronic path lies not only in its mathematical elegance but also in its implications for physics. It showcases the relationship between speed, gravity, and the shape of a trajectory. When an object moves along this optimal path, it accelerates due to gravitational force, allowing it to reach its destination faster than if it followed a straight line or any other route. This principle can be observed in various fields, including astronomy, where celestial bodies follow paths that minimize their travel time through space.Moreover, the brachistochronic path serves as a foundation for understanding more complex systems in physics. By studying the properties of this path, scientists can gain insights into topics such as energy conservation, momentum, and the behavior of particles in motion. It also highlights the importance of calculus and optimization in solving real-life problems, emphasizing how mathematical tools can lead to practical solutions.In conclusion, the concept of a brachistochronic path is a remarkable intersection of mathematics and physics, offering valuable lessons about motion and optimization. Understanding this principle not only enhances our knowledge of physical laws but also encourages innovative thinking in engineering and design. As we continue to explore the universe and develop new technologies, the principles underlying the brachistochronic path will undoubtedly play a vital role in shaping our future endeavors. The journey of learning about such concepts enriches our understanding of the world around us, showing us that even the simplest questions can lead to profound discoveries.

在物理和数学的世界中，“brachistochronic path”这一概念在理解运动和优化方面发挥着至关重要的作用。术语“brachistochrone”源自希腊语单词“brachistos”，意为最短，而“chronos”意为时间。因此，“brachistochronic path”指的是一个物体在重力影响下从一点到另一点所采取的最小化所需时间的路径。这个迷人的问题最早由约翰·伯努利于1696年提出，自那时起就吸引了数学家和物理学家的注意。要理解“brachistochronic path”的重要性，必须考虑其在现实场景中的应用。想象一下，一个过山车需要将乘客从山顶运输到地面。如果目标是最小化旅行时间，那么轨道的设计必须遵循一种特定的曲线，称为摆线。这条曲线是brachistochrone问题的解决方案，展示了数学原理如何应用于工程和设计。“brachistochronic path”的美丽不仅在于其数学优雅，还在于其对物理学的影响。它展示了速度、重力和轨迹形状之间的关系。当一个物体沿着这条最佳路径移动时，由于重力的作用，它会加速，从而使它比沿直线或其他路径更快地到达目的地。这个原理可以在各个领域观察到，包括天文学，天体在空间中遵循的路径最小化了它们的旅行时间。此外，“brachistochronic path”作为理解物理学中更复杂系统的基础。通过研究这条路径的特性，科学家可以获得关于能量守恒、动量以及运动粒子行为等主题的洞察。它还强调了微积分和优化在解决现实问题中的重要性，强调了数学工具如何导致实际解决方案。总之，“brachistochronic path”的概念是数学和物理的一个显著交汇点，提供了关于运动和优化的宝贵教训。理解这一原则不仅增强了我们对物理法则的认识，而且鼓励在工程和设计中的创新思维。随着我们继续探索宇宙并开发新技术，“brachistochronic path”背后的原则无疑将在塑造我们未来的努力中发挥重要作用。了解这些概念的旅程丰富了我们对周围世界的理解，向我们展示了即使是最简单的问题也能导致深刻的发现。