Newton-Euler Equations for a Rigid Body - Center of Mass & Inertia Tensor Calculation Worked Example

Rigid bodies made of a continuous mass distribution are considered. We write the formulas for the total mass and center of mass. .
flat triangular plate of uniform density and use integrals do determine the center of mass. We discuss the idea of decomposing our a complicated rigid body into simpler rigid bodies for purposes of calculating the mass moments (such as the location of the center of mass and the moment of inertia tensor). .
Composite shapes: complicated rigid body approximated by simpler ones to estimate center of mass and moment of inertia.
The Newton-Euler approach to rigid body dynamics is introduced, including Euler's 1st Law for translational motion (a.k.a., the "superparticle theorem") and Euler's 2nd Law for rotational motion (a.k.a., the rotational dynamics equation, Euler's rotational equation). .
Parallels between the kinematic and dynamic equations of the translational and rotational motion of a rigid body..
The mass moments of a rigid body are summarized:.
Euler's 2nd Law, the rotational dynamics equation, in the body-fixed frame, and as a set of 3 first-order ODEs for the components of angular velocity..