anholonomic coordinate

简明释义

非完整坐标;

英英释义

例句

1.In classical mechanics, anholonomic coordinates 非完整坐标 are essential for systems with constraints that depend on the path taken.

在经典力学中，anholonomic coordinates 非完整坐标 对于依赖于路径的约束系统至关重要。

2.The formulation of the equations of motion can be simplified by choosing appropriate anholonomic coordinates 非完整坐标.

通过选择合适的anholonomic coordinates 非完整坐标，可以简化运动方程的公式。

3.The dynamics of a rolling ball can be analyzed using anholonomic coordinates 非完整坐标 to account for its constraints.

可以使用anholonomic coordinates 非完整坐标 分析滚动球的动力学，以考虑其约束条件。

4.In robotics, the use of anholonomic coordinates 非完整坐标 allows for more flexible movement of robotic arms.

在机器人技术中，使用anholonomic coordinates 非完整坐标 可以使机器人手臂的运动更加灵活。

5.In the study of non-linear systems, anholonomic coordinates 非完整坐标 provide a powerful tool for analysis.

在非线性系统的研究中，anholonomic coordinates 非完整坐标 提供了一种强大的分析工具。

作文

In the realm of physics and mathematics, the concept of coordinates plays a crucial role in understanding the dynamics of systems. One particularly interesting type of coordinate system is known as an anholonomic coordinate. This term refers to a type of coordinate system where the coordinates cannot be expressed as functions of each other. Unlike holonomic coordinates, which are dependent on a set of constraints that can be expressed as equations, anholonomic coordinates do not adhere to such relationships. This distinction is fundamental in fields like classical mechanics and differential geometry.To illustrate the importance of anholonomic coordinates, consider the example of a particle moving on a surface. If the motion of the particle is constrained by certain conditions, we can describe its position using holonomic coordinates. However, if we introduce additional constraints that depend on the velocity or path taken by the particle rather than just its position, we enter the realm of anholonomic coordinates. In this case, the coordinates may involve integrals of the velocities, making them more complex and less intuitive.The implications of using anholonomic coordinates extend beyond mere mathematical abstraction; they have practical applications in various fields, including robotics and control theory. For instance, when designing a robotic arm, engineers often encounter situations where the movement of the arm cannot be easily described by simple positional coordinates. Instead, they must account for the arm's orientation and the paths it can take, which leads to the use of anholonomic coordinates.Furthermore, the study of anholonomic coordinates helps us understand the nature of constraints in dynamical systems. In many cases, systems governed by anholonomic coordinates exhibit unique behaviors that differ from those described by traditional holonomic systems. For example, in non-conservative systems where energy is not conserved, the equations of motion become more complicated when expressed in terms of anholonomic coordinates. This complexity can lead to fascinating phenomena, such as the emergence of chaotic behavior in certain systems.Another area where anholonomic coordinates come into play is in the formulation of Lagrangian mechanics. In this framework, the equations of motion are derived from the principle of least action. When dealing with anholonomic coordinates, the variational principles must be adapted to accommodate the additional constraints imposed by the system. This adaptation can lead to new insights and techniques for solving complex physical problems.In conclusion, the concept of anholonomic coordinates is an essential aspect of advanced physics and mathematics. By understanding how these coordinates function and their implications in various fields, we can gain deeper insights into the behavior of complex systems. Whether in robotics, classical mechanics, or theoretical physics, the study of anholonomic coordinates continues to challenge our understanding and expand our capabilities in modeling and controlling dynamic systems. As we advance in technology and our understanding of the universe, the relevance of anholonomic coordinates will undoubtedly grow, paving the way for new discoveries and innovations.

在物理学和数学领域，坐标的概念在理解系统的动态中起着至关重要的作用。一个特别有趣的坐标系统被称为非全局坐标。这个术语指的是一种坐标系统，其中坐标不能相互表示为函数。与可以用方程表达的约束依赖的全局坐标不同，非全局坐标不遵循这样的关系。这一区别在经典力学和微分几何等领域是基本的。为了说明非全局坐标的重要性，考虑一个在表面上移动的粒子的例子。如果粒子的运动受到某些条件的限制，我们可以用全局坐标来描述它的位置。然而，如果我们引入依赖于粒子速度或路径的额外约束，而不仅仅是位置，我们就进入了非全局坐标的领域。在这种情况下，坐标可能涉及速度的积分，使其更加复杂且不易直观理解。使用非全局坐标的影响超出了单纯的数学抽象；它们在机器人技术和控制理论等多个领域具有实际应用。例如，在设计机器人手臂时，工程师经常遇到运动无法通过简单的位置信息轻易描述的情况。相反，他们必须考虑手臂的方向和可以采取的路径，这导致了非全局坐标的使用。此外，非全局坐标的研究帮助我们理解动态系统中约束的性质。在许多情况下，由非全局坐标支配的系统表现出与传统全局系统不同的独特行为。例如，在能量不守恒的非保守系统中，当用非全局坐标表示运动方程时，方程变得更加复杂。这种复杂性可能导致某些系统中混沌行为的出现。另一个涉及非全局坐标的领域是拉格朗日力学的公式化。在这个框架中，运动方程是从最小作用原理中推导出来的。当处理非全局坐标时，变分原理必须进行调整以适应系统施加的附加约束。这种调整可以为解决复杂物理问题提供新的见解和技术。总之，非全局坐标的概念是高级物理学和数学的重要方面。通过理解这些坐标如何运作及其在各个领域的影响，我们可以对复杂系统的行为获得更深刻的见解。无论是在机器人技术、经典力学还是理论物理中，对非全局坐标的研究继续挑战我们的理解，并扩展我们在建模和控制动态系统中的能力。随着我们在技术和对宇宙理解上的进步，非全局坐标的相关性无疑将会增长，为新的发现和创新铺平道路。