holonomic condition; condition for completeness

简明释义

完全性条件

英英释义

例句

1.In robotics, the design of a manipulator must satisfy the holonomic condition 全局约束条件 to ensure that it can reach any point in its workspace.

在机器人技术中，机械手臂的设计必须满足holonomic condition 全局约束条件，以确保它可以到达工作空间中的任何点。

2.When modeling a dynamic system, we need to verify that it meets the holonomic condition 全局约束条件 to simplify the equations of motion.

在建模动态系统时，我们需要验证它是否满足holonomic condition 全局约束条件以简化运动方程。

3.The holonomic condition 全局约束条件 is crucial when analyzing the motion of a particle constrained to move on a surface.

在分析受限于在表面上移动的粒子的运动时，holonomic condition 全局约束条件是至关重要的。

4.For a mechanical system to be described accurately, it should fulfill the condition for completeness 完备性条件 which ensures all necessary constraints are included.

为了准确描述一个机械系统，它应该满足condition for completeness 完备性条件，以确保包含所有必要的约束。

5.In control theory, ensuring the condition for completeness 完备性条件 is essential for the stability of the system.

在控制理论中，确保condition for completeness 完备性条件对于系统的稳定性至关重要。

作文

In the field of physics and mathematics, particularly in the study of mechanics, the concept of constraints plays a pivotal role. Constraints are conditions that limit the motion of a system, and they can be classified into various types. Among these, the terms holonomic condition and condition for completeness stand out as essential concepts for understanding the behavior of dynamical systems. A holonomic condition refers to a constraint that can be expressed as an equation involving only the coordinates of the system and time, which means that the constraint can be integrated to yield a relationship among the coordinates. This type of constraint is crucial because it allows for the possibility of expressing the system's configuration in a reduced form, simplifying the analysis of its dynamics. For example, consider a pendulum swinging in a vertical plane. The constraint that the length of the pendulum remains constant is a holonomic condition because it can be described by an equation relating the position of the pendulum to time, thus allowing us to express its motion in terms of fewer variables.On the other hand, the condition for completeness pertains to the sufficiency of the constraints imposed on a system. A system is said to satisfy the condition for completeness if the number of independent constraints matches the number of degrees of freedom of the system. In simpler terms, this means that all possible motions of the system are accounted for by the constraints. If a system does not meet this condition, it may have redundant or insufficient constraints, leading to ambiguity in its motion. For instance, in a mechanical system with two degrees of freedom, if there are exactly two independent constraints, then the system satisfies the condition for completeness. However, if there are three constraints, one of them must be dependent on the others, indicating that the system does not have a complete set of constraints.Understanding these concepts is vital for engineers and physicists who analyze complex systems. When designing mechanical structures or robotic systems, ensuring that the constraints are holonomic conditions and that they meet the condition for completeness is critical for predicting how the system will behave under various forces and movements. Failure to do so could lead to unexpected behaviors, such as instability or failure to perform desired tasks. Therefore, the application of holonomic condition and condition for completeness is not merely theoretical; it has practical implications in fields ranging from robotics to aerospace engineering.In conclusion, the terms holonomic condition and condition for completeness are fundamental in the study of constrained systems in mechanics. They help in simplifying the analysis of motion and ensuring that all aspects of a system's behavior are accurately represented. As technology advances and systems become more complex, the importance of these concepts will continue to grow, making it essential for future scientists and engineers to grasp their significance thoroughly.

在物理学和数学领域，特别是在力学研究中，约束的概念发挥着关键作用。约束是限制系统运动的条件，可以分为各种类型。在这些约束中，术语holonomic condition（全约束条件）和condition for completeness（完备性条件）作为理解动态系统行为的基本概念而脱颖而出。holonomic condition指的是可以仅用系统的坐标和时间表示的约束，这意味着该约束可以被积分，从而得出坐标之间的关系。这种类型的约束至关重要，因为它允许以简化的形式表达系统的配置，从而简化其动力学分析。例如，考虑一个在垂直平面内摆动的摆。摆的长度保持恒定的约束是一个holonomic condition，因为它可以通过一个与摆的位置和时间相关的方程来描述，从而使我们能够用更少的变量来表达其运动。另一方面，condition for completeness（完备性条件）涉及对系统施加的约束的充分性。当独立约束的数量与系统的自由度数量相匹配时，系统被认为满足condition for completeness。简单来说，这意味着所有系统的可能运动都由约束所涵盖。如果一个系统不满足这个条件，它可能具有冗余或不足的约束，从而导致其运动的不确定性。例如，在一个具有两个自由度的机械系统中，如果恰好有两个独立的约束，那么该系统满足condition for completeness。然而，如果有三个约束，其中一个必须依赖于其他约束，这表明该系统没有完整的约束集。理解这些概念对于分析复杂系统的工程师和物理学家至关重要。在设计机械结构或机器人系统时，确保约束是holonomic conditions并且满足condition for completeness对于预测系统在各种力和运动下的行为至关重要。未能做到这一点可能会导致意外的行为，例如不稳定性或无法执行预期任务。因此，holonomic condition和condition for completeness的应用不仅仅是理论上的；它在从机器人技术到航空航天工程等领域具有实际意义。总之，术语holonomic condition和condition for completeness在力学中的约束系统研究中是基本的。它们有助于简化运动分析，并确保系统行为的所有方面都得到准确表示。随着技术的发展和系统变得越来越复杂，这些概念的重要性将继续增长，使未来的科学家和工程师必须彻底掌握它们的意义。