Moment of Inertia Matrix
The scalar moments of inertia appear as elements in a matrix when a system of particles is assembled into a rigid body that moves in three dimensional space. This inertia matrix appears in the calculation of the angular momentum, kinetic energy and resultant torque of the rigid system of particles.
An important application of the inertia matrix and Newton's laws of motion is the analysis of a spinning top. This is discussed in the article on Gyroscopic precession. A more detailed presentation can be found in the article on Euler's equations of motion.
Let the system of particles Pi, i = 1,..., n be located at the coordinates ri with velocities vi relative to a fixed reference frame. For a (possibly moving) reference point R, the relative positions are
and the (absolute) velocities are
where ω is the angular velocity of the system, and V is the velocity of R.
Read more about this topic: Inertia Tensor
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