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所在平台: Udemy |
课程主页: https://www.udemy.com/course/advanced-classical-mechanics/
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**课程名称：高等经典力学** **课程概述：** 本课程深入探讨了经典力学的核心概念和高级主题。 * **中心力运动：** 课程始于对粒子在中心力作用下的运动分析。中心力是一种保守的无旋力，始终沿径向作用，可以是吸引力或排斥力。在中心力作用下，粒子的运动将被限制在一个平面内，其轨迹二维。能量和角动量守恒限制了这种运动。行星和卫星的运动是中心力问题的典型应用。 * **约束运动：** 接下来，课程讨论了约束运动的特征，即运动受到一个或多个条件的限制。这些约束力是“无做功力”。课程分析了多种保守的完整约束系统。 * **变分法与拉格朗日力学：** 课程介绍了欧拉的变分法基本概念，并将其应用于构建第二代经典力学——拉格朗日力学。通过广义坐标和其他广义参数，我们学习了完整保守系统的拉格朗日量。课程详细推导了第一类和第二类拉格朗日方程，并将其应用于多个保守完整系统。 * **哈密顿力学：** 最后，通过勒让德变换定义了系统的哈密顿量，并从哈密顿量的基本特性推导出了第三代经典力学——哈密顿力学的正则方程。这些正则方程随后被用于分析多个保守系统。
In this content - Advanced Classical Mechanics, we have started our discussion with particle motion under central force. This central force is a conservative irrotational force which always acts along the radial sense and it may be attractive or repulsive. Under action of this central force, the motion of the particle will become confined in a plane and the orbit of the particle must lie in two dimension. The motion will be restricted with energy and angular momentum conservation and here the best application of such central force problem is on the motion of planet and satellite. After that we have discussed the features of constrained motion where the motion is restricted by at least one or more than one condition or restriction. For such constrained motion, the corresponding constraint will be hold by the force of constraint which is itself no work force. Here a several conservative holonomic systems are made analyzed in this constrained motion. On the other hand, in this content, we have discussed the basic concept of Calculus of Variation as given by Euler and the concept is fully applied to the second generation of Classical Mechanics, known as Lagrangian Dynamics through the concept of Lagrangian of a holonomic conservative system by proper use of generalized coordinates and other generalized parameters. Lagrange's equation of both 1st and 2nd kind are made developed in several way and then is applied to several conservative holonomic system. At the end of this content, the Hamiltonian of the system is made defined through Legendre dual transformation and after that Hamilton's canonical equations of Hamiltonian dynamics which is specifically 3rd generation of Classical Mechanics are obtained from basic characteristics of Hamiltonian and finally these canonical equations are made applied for analyzing several conservative systems.
