linearisation

简明释义

英[ˌlɪnɪəraɪˈzeɪʃən]美[ˌlɪnɪərɪˈzeʃən]

n. 线性化

英英释义

单词用法

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例句

1.The range of linearisation and testing standard of the motor is also presented.

还介绍了电动机的线性化范围和测试标准。

2.The range of linearisation and testing standard of the motor is also presented.

还介绍了电动机的线性化范围和测试标准。

3.The linearisation of the model allowed us to apply linear regression techniques effectively.

模型的线性化使我们能够有效地应用线性回归技术。

4.The linearisation of the function around a specific point can provide valuable insights.

在特定点附近的函数线性化可以提供有价值的见解。

5.In engineering, linearisation helps in predicting system behavior under small perturbations.

在工程中，线性化有助于预测系统在小扰动下的行为。

6.The process of linearisation is essential in simplifying complex equations for easier analysis.

对复杂方程进行线性化的过程对于简化分析至关重要。

7.Scientists often use linearisation to approximate non-linear systems for easier computation.

科学家们常常使用线性化来近似非线性系统，以便于计算。

作文

In the realm of mathematics and engineering, the concept of linearisation plays a crucial role in simplifying complex systems. Linearisation (线性化) refers to the process of approximating a nonlinear function by a linear function around a specific point. This technique is particularly useful because many real-world phenomena can be modeled using nonlinear equations, which are often difficult to solve analytically. By applying linearisation, we can transform these challenging problems into more manageable linear equations that are easier to analyze and solve.One of the most common applications of linearisation occurs in control theory. Engineers often need to design controllers for systems that exhibit nonlinear behavior, such as robotic arms or aircraft. By performing linearisation on the system's equations of motion, they can develop linear control strategies that are effective in a limited range of operation. For instance, when designing an autopilot system for an aircraft, engineers might linearise the aircraft's dynamics around a stable flight condition. This allows them to use well-established linear control techniques, ensuring that the aircraft responds predictably to pilot inputs.Another area where linearisation proves invaluable is in optimization problems. Many optimization algorithms rely on the assumption that the functions being optimized are linear. However, in practice, these functions are often nonlinear. By applying linearisation, we can approximate these nonlinear functions as linear ones, enabling the use of efficient optimization techniques. For example, in economic modeling, demand functions are frequently nonlinear. Economists can use linearisation to simplify their models, making it easier to derive insights about consumer behavior and market dynamics.Additionally, linearisation is essential in the field of physics, particularly in the study of mechanics. When analyzing the motion of objects under the influence of forces, the equations governing their motion may be nonlinear. By linearising these equations, physicists can gain a clearer understanding of the underlying principles and predict the behavior of physical systems under small perturbations. This approach is vital in fields such as structural engineering, where the response of materials to stress must be understood to prevent failure.Despite its usefulness, linearisation has limitations. The accuracy of the linear approximation depends on the choice of the point around which the function is linearized. If the system operates far from this point, the linear model may not accurately represent the behavior of the original nonlinear system. Therefore, it is essential to consider the range of validity when applying linearisation. In some cases, higher-order terms may need to be included to improve the approximation.In conclusion, linearisation (线性化) is a powerful mathematical tool that simplifies the analysis of complex systems across various fields, including engineering, economics, and physics. By transforming nonlinear equations into linear ones, linearisation enables researchers and engineers to apply established techniques to solve problems that would otherwise be intractable. However, it is crucial to understand the limitations of this approach and to carefully consider the context in which linearisation is applied. As we continue to encounter complex systems in our increasingly technological world, the importance of mastering linearisation cannot be overstated.