Newton-Euler Equations for a Rigid Body - Center of Mass & Inertia Tensor Calculation Worked Example
Dive into a comprehensive lecture on Newton-Euler equations for rigid bodies, focusing on center of mass and inertia tensor calculations. Explore the formulas for total mass and center of mass in continuous mass distributions. Work through a detailed example of calculating the center of mass for a flat triangular plate using integrals. Learn about decomposing complex rigid bodies into simpler shapes for mass moment calculations. Understand the Newton-Euler approach to rigid body dynamics, including Euler's 1st and 2nd Laws. Examine the parallels between translational and rotational motion equations. Study the mass moments of rigid bodies, from total mass to moment of inertia. Conclude with an analysis of Euler's 2nd Law in the body-fixed frame and its representation as first-order ODEs for angular velocity components.