d'alembert's principle

简明释义

达兰贝尔原理

英英释义

例句

1.The use of d'alembert's principle allows engineers to derive equations of motion more easily.

使用d'alembert's principle（达朗贝尔原理）可以让工程师更轻松地推导运动方程。

2.In classical mechanics, we often apply d'alembert's principle to simplify the analysis of complex systems.

在经典力学中，我们经常应用d'alembert's principle（达朗贝尔原理）来简化复杂系统的分析。

3.When studying vibrations, applying d'alembert's principle can help in understanding the system's behavior.

在研究振动时，应用d'alembert's principle（达朗贝尔原理）可以帮助理解系统的行为。

4.In robotics, d'alembert's principle is used to model the motion of robotic arms.

在机器人技术中，d'alembert's principle（达朗贝尔原理）用于建模机械臂的运动。

5.The formulation of dynamics often involves d'alembert's principle to account for inertial forces.

动力学的公式化通常涉及d'alembert's principle（达朗贝尔原理）以考虑惯性力。

作文

In the realm of classical mechanics, the understanding of motion and forces is fundamental to the study of physical systems. One of the pivotal concepts that emerged from the works of early mathematicians and physicists is d'Alembert's principle. This principle, named after the French mathematician Jean le Rond d'Alembert, provides a powerful framework for analyzing dynamic systems by combining Newton's laws of motion with a broader perspective on forces and energy. d'Alembert's principle states that the sum of the differences between the forces acting on a system and the inertial forces is zero. This can be expressed mathematically as F - ma = 0, where F represents the total force applied to the system, m is the mass, and a is the acceleration. This relationship allows us to consider both the external forces and the effects of inertia simultaneously, making it particularly useful in solving complex mechanical problems.The significance of d'Alembert's principle extends beyond mere theoretical exploration; it serves as a bridge between dynamics and statics. By transforming a dynamic problem into a static one, it simplifies the analysis of systems in motion. For instance, when engineers design structures or vehicles, they often encounter situations where multiple forces act simultaneously. Using d'Alembert's principle, they can calculate the resultant forces and predict the behavior of the system under various conditions.Moreover, d'Alembert's principle is instrumental in the development of Lagrangian mechanics, which is a reformulation of classical mechanics. This approach emphasizes energy conservation and provides a more generalized method for deriving the equations of motion. In Lagrangian mechanics, the principle of least action is utilized, which states that the path taken by a system is the one that minimizes the action, a quantity derived from the kinetic and potential energies of the system. Here, d'Alembert's principle plays a crucial role in establishing the connection between forces and energy, allowing physicists to derive equations of motion without directly referencing the forces acting on the system.In practical applications, d'Alembert's principle is widely used in engineering fields, especially in robotics and aerospace. For example, when designing robotic arms, engineers must account for various forces, including gravitational and inertial forces, to ensure precise movements. By applying d'Alembert's principle, they can effectively model the dynamics of the robotic system and optimize its performance. Similarly, in aerospace engineering, this principle aids in analyzing the forces acting on aircraft during flight, helping to ensure stability and control.In conclusion, d'Alembert's principle is a cornerstone of classical mechanics that enhances our understanding of motion and forces in physical systems. Its ability to unify the concepts of dynamics and statics makes it an invaluable tool for scientists and engineers alike. As we continue to explore the complexities of the physical world, the principles established by d'Alembert will undoubtedly remain relevant, guiding future innovations and discoveries in mechanics and beyond.

在经典力学的领域中，运动和力的理解是研究物理系统的基础。早期数学家和物理学家的工作中出现的一个关键概念是d'Alembert's principle（达朗贝尔原理）。这个以法国数学家让·勒·隆·达朗贝尔命名的原理，为通过将牛顿运动定律与更广泛的力和能量视角结合起来来分析动态系统提供了一个强有力的框架。d'Alembert's principle指出，作用于系统的力与惯性力之间的差的总和为零。这可以用数学表达为F - ma = 0，其中F代表施加于系统的总力，m是质量，a是加速度。这个关系使我们能够同时考虑外部力和惯性的影响，从而在解决复杂机械问题时特别有用。d'Alembert's principle的重要性超越了单纯的理论探索；它在动力学和静力学之间架起了一座桥梁。通过将动态问题转化为静态问题，它简化了运动系统的分析。例如，当工程师设计结构或车辆时，他们常常会遇到多个力同时作用的情况。利用d'Alembert's principle，他们可以计算合力并预测系统在各种条件下的行为。此外，d'Alembert's principle在拉格朗日力学的发展中也发挥了重要作用，拉格朗日力学是经典力学的一种重新表述。这种方法强调能量守恒，并为推导运动方程提供了一种更为广泛的方法。在拉格朗日力学中，最小作用量原理被用来说明，系统所采取的路径是最小化作用量的路径，作用量是由系统的动能和势能推导出的量。在这里，d'Alembert's principle在建立力与能量之间的联系中发挥了关键作用，使物理学家能够推导出运动方程，而无需直接引用作用于系统的力。在实际应用中，d'Alembert's principle在工程领域得到了广泛应用，尤其是在机器人技术和航空航天领域。例如，在设计机器人手臂时，工程师必须考虑各种力，包括重力和惯性力，以确保精确的运动。通过应用d'Alembert's principle，他们能够有效地建模机器人系统的动态并优化其性能。同样，在航空航天工程中，这一原理有助于分析飞行中飞机所受的力，帮助确保稳定性和控制。总之，d'Alembert's principle是经典力学的基石，增强了我们对物理系统中运动和力的理解。它将动力学和静力学的概念统一在一起，使其成为科学家和工程师不可或缺的工具。随着我们继续探索物理世界的复杂性，达朗贝尔建立的原理无疑将保持其相关性，引导未来在力学及其他领域的创新和发现。