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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/analytical-mechanics-spacecraft-dynamics
课程评论：没有评论
课程名称：航天器动力学的分析力学 概述：本课程是“高级航天器动力学与控制”专业中的第二部分。课程假设学员具备扎实的航天器动力学和控制基础，包括粒子动力学、旋转框架、刚体运动学和动力学。课程重点在于理解关键的分析力学方法，以代数高效的方式开发运动方程。课程首先讨论达朗贝尔原理，以及与之相关的虚功和虚位移概念，这使我们能够忽略非做功力项。接着，探讨无约束系统和全约束系统。随后，简要回顾凯恩方程和达朗贝尔方程的虚功形式，适用于粒子系统。 接下来，发展拉格朗日方程，仍然假设有限的一组广义坐标，但也可应用于多个刚体。拉格朗日乘数用于施加法夫约束。 最后，发展哈密顿扩展原理，以考虑具有柔性组件的动力系统，拥有无限的自由度。课程主要聚焦于如何建立与航天器相关的偏微分方程，但不研究其数值解。课程最后比较了假设模式方法与经典有限元解法。 课程大纲： 第1部分：分析力学的广义方法 描述：学习使用达朗贝尔原理、虚功形式、拉格朗日方程以及玻尔兹曼-哈梅尔方程开发运动方程的方法。这些方法允许更高效地开发运动方程，考虑状态基础（全约束）和速率基础（法夫约束）。 第2部分：基于能量的运动方程 描述：推导基于能量表达的有限自由度动力系统的运动方程开发方法。 第3部分：分析动力学中的变分方法 描述：学习为具有变形形状的动力系统开发运动方程。这类系统具有无限自由度，并导致偏微分方程。
Part: 1
Title: Generalized Methods of Analytical Mechanics
Description:Learn the methodology of developing equations of motion using D'Alembert's principle, virtual power forms, Lagrange's equations as well as the Boltzmann-Hamel equations. These methods allow for more efficient equations of motion development where state based (holonomic) and rate based (Pfaffian constraints) are considered.
Part: 2
Title:Energy Based Equations of Motion
Description:Derive methods to develop the equations of motion of a dynamical system with finite degrees of freedom based on energy expressions.
Part: 3
Title:Variational Methods in Analytical Dynamics
Description:Learn to develop the equations of motion for a dynamical system with deformable shapes. Such systems have infinite degrees of freedom and lead to partial differential equations.
This course is part 2 of the specialization Advanced Spacecraft Dynamics and Control. It assumes you have a strong foundation in spacecraft dynamics and control, including particle dynamics, rotating frame, rigid body kinematics and kinetics. The focus of the course is to understand key analytical mechanics methodologies to develop equations of motion in an algebraically efficient manner. The course starts by first developing D’Alembert’s principle and how the associated virtual work and virtual displacement concepts allows us to ignore non-working force terms. Unconstrained systems and holonomic constrains are investigated. Next Kane's equations and the virtual power form of D'Alembert's equations are briefly reviewed for particles. Next Lagrange’s equations are developed which still assume a finite set of generalized coordinates, but can be applied to multiple rigid bodies as well. Lagrange multipliers are employed to apply Pfaffian constraints. Finally, Hamilton’s extended principle is developed to allow us to consider a dynamical system with flexible components. Here there are an infinite number of degrees of freedom. The course focuses on how to develop spacecraft related partial differential equations, but does not study numerically solving them. The course ends comparing the presented assumed mode methods to classical final element solutions.
