secular equation

简明释义

久期方程

英英释义

例句

1.The mathematician derived a secular equation 世俗方程 to model the population growth over decades.

这位数学家推导出一个 secular equation 世俗方程 来模拟几十年的人口增长。

2.Research in climate science often involves solving a secular equation 世俗方程 to understand long-term climate patterns.

气候科学研究通常涉及解决一个 secular equation 世俗方程 以理解长期气候模式。

3.In astrophysics, a secular equation 世俗方程 helps predict the orbits of celestial bodies over time.

在天体物理学中，secular equation 世俗方程 有助于预测天体随时间的轨道。

4.The secular equation 世俗方程 for this economic model reveals trends that can inform policy decisions.

这个经济模型的 secular equation 世俗方程 显示出可以为政策决策提供信息的趋势。

5.In physics, a secular equation 世俗方程 can describe the long-term behavior of a system under certain conditions.

在物理学中，secular equation 世俗方程 可以描述在特定条件下系统的长期行为。

作文

In the realm of mathematics, particularly in the study of differential equations, one often encounters various types of equations that govern the behavior of dynamic systems. Among these, the term secular equation refers to a specific class of equations that emerge in the context of perturbation theory. Perturbation theory is a mathematical technique used to find an approximate solution to a problem that cannot be solved exactly. The secular equation plays a crucial role in determining the stability and long-term behavior of solutions to these problems.To understand the significance of the secular equation, it is essential to recognize its application in various scientific fields, including physics, engineering, and even economics. For instance, in celestial mechanics, the secular equation helps in predicting the orbits of celestial bodies over extended periods. By analyzing the perturbations in their motion due to gravitational interactions, scientists can derive the secular equation to ascertain how these bodies will behave over time.The derivation of the secular equation typically involves identifying a small parameter that represents a slight change in the system's conditions. This small parameter allows mathematicians to expand the solution in a series, leading to the formation of the secular equation. The solutions to this equation provide insights into the stability of the system. If the solutions indicate that the perturbations grow indefinitely, the system is deemed unstable; conversely, if they remain bounded, the system is stable.Moreover, the concept of the secular equation extends beyond theoretical applications. In engineering, for example, the secular equation is utilized in control systems to ensure that feedback mechanisms maintain stability in the face of external disturbances. Understanding how to manipulate and solve the secular equation is vital for engineers who design systems that must operate reliably under varying conditions.In economics, the secular equation can also find its place in modeling dynamic systems that describe economic growth or market behavior. Economists may use the secular equation to analyze long-term trends and cycles, helping policymakers make informed decisions based on predicted future states of the economy.In conclusion, the secular equation is a fundamental concept in mathematics that has far-reaching implications across various disciplines. Its ability to provide insights into the stability and behavior of dynamic systems makes it an invaluable tool for researchers and practitioners alike. As we continue to explore the complexities of the universe, the importance of the secular equation in understanding and predicting system behaviors cannot be overstated. Whether in the context of celestial mechanics, engineering, or economics, mastering the secular equation is essential for anyone looking to delve deeper into the intricacies of mathematical modeling and analysis.

在数学领域，特别是在微分方程的研究中，人们经常会遇到各种类型的方程，这些方程支配着动态系统的行为。在这些方程中，术语secular equation指的是在摄动理论背景下出现的一类特定方程。摄动理论是一种数学技术，用于找到无法精确求解的问题的近似解。secular equation在确定这些问题的解的稳定性和长期行为方面起着至关重要的作用。要理解secular equation的重要性，必须认识到它在物理学、工程学甚至经济学等各个科学领域的应用。例如，在天体力学中，secular equation有助于预测天体在较长时间内的轨道。通过分析由于引力相互作用而导致的运动扰动，科学家可以推导出secular equation以确定这些天体将如何随时间变化。secular equation的推导通常涉及识别一个小参数，该参数表示系统条件的轻微变化。这个小参数使数学家能够将解展开为级数，从而形成secular equation。该方程的解提供了对系统稳定性的见解。如果解表明扰动无限增长，则该系统被认为是不稳定的；反之，如果它们保持有界，则该系统是稳定的。此外，secular equation的概念超越了理论应用。在工程中，例如，secular equation被用于控制系统，以确保反馈机制在外部干扰下保持稳定。理解如何操纵和求解secular equation对设计必须在不同条件下可靠运行的系统的工程师至关重要。在经济学中，secular equation也可以在建模描述经济增长或市场行为的动态系统中找到其位置。经济学家可能会使用secular equation来分析长期趋势和周期，帮助决策者根据预测的经济未来状态做出明智的决策。总之，secular equation是数学中的一个基本概念，在各个学科中具有深远的影响。它提供的对动态系统的稳定性和行为的见解，使其成为研究人员和从业人员不可或缺的工具。随着我们继续探索宇宙的复杂性，secular equation在理解和预测系统行为方面的重要性不容低估。无论是在天体力学、工程学还是经济学的背景下，掌握secular equation对于任何希望深入研究数学建模和分析复杂性的人来说都是必不可少的。