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所在平台: Udemy |
课程主页: https://www.udemy.com/course/advanced-rigid-body-mechanics-in-three-dimensions/
课程评论：没有评论
**课程名称：** 三维刚体动力学高级 **课程概述：** 本课程深入探讨支配刚体运动的基本方程和概念。课程将从第一性原理出发，全面详细地推导所有关键方程，确保学生理解其底层原理。 **先修要求：** * **数学：** 向量、点积与叉积、基础线性代数（矩阵、行列式、特征向量、特征值）、基础微积分（导数和体积积分）。 * **物理：** 熟悉牛顿运动定律，特别是点粒子动力学（F = ma）。 **课程内容：** * 将点粒子动力学扩展应用于刚体运动。 * 推导惯性矩阵 (inertia matrix)，及其在力矩方程和刚体动能表达式中的作用。 * 引入角速度 (angular velocity) 概念，并证明其唯一性。 * 推导连接刚体上任意两点速度和加速度的关键运动学公式。 * 推导 Chasles 定理（或称 Mozzi-Chasles 定理），该定理指出刚体的任意位移可分解为沿特定轴（Mozzi 轴）的平移和绕同一轴的转动。 **学习目标：** 完成本课程后，学生将对支配刚体运动的数学和物理原理有深刻的理解，为在力学、机器人学和工程学等领域的深入学习奠定坚实基础。
This course delves into the fundamental equations and concepts that govern the mechanics of rigid bodies. It provides a comprehensive and detailed derivation of all key equations, ensuring that students understand the underlying principles from first principles. To fully engage with the material, a solid understanding of the following mathematical concepts is required: vectors, dot and cross products, basic linear algebra (including matrices, determinants, eigenvectors, and eigenvalues), and essential calculus (with a focus on derivatives and volume integrals). On the physics side, the only prerequisite is familiarity with Newton's laws of motion, as they serve as the foundational framework for the entire course. Specifically, the laws governing point-particle dynamics (F = ma, where F is the total force acting on a particle, m is its mass, and a is its acceleration) are extended to construct the equations governing rigid body motion.Throughout the course, we will derive the inertia matrix, which plays a crucial role in the equation of moments and in the expression of the kinetic energy of a rigid body. The concept of angular velocity will also be introduced, and its uniqueness will be demonstrated, setting the stage for a deeper understanding of rotational dynamics. Additionally, we will explore several important kinematic formulas that relate the velocities and accelerations of arbitrary points on a rigid body.One of the key highlights of the course is the derivation of Chasles' theorem (also known as Mozzi-Chasles' theorem), which states that the most general displacement of a rigid body can be achieved by combining a translation along a line, known as the Mozzi axis, with a rotation about the same axis. This result has profound implications for the analysis of rigid body motion and serves as a cornerstone for further study in mechanics.By the end of the course, students will gain a deep understanding of the mathematical and physical principles that govern the motion of rigid bodies, laying a strong foundation for advanced studies in mechanics, robotics, and engineering applications.
