Advanced Rigid Body Mechanics in Three Dimensions

Advanced Rigid Body Mechanics in Three Dimensions udemy course free download

Mathematical intuition behind the fundamental equations in rigid body mechanics

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.