Moment of Inertia - Moment of Inertia Matrix

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. Let the system of particles Pi, i=1,...,n be located at the coordinates ri and velocities vi. Select a reference point R and compute the relative position and velocity vectors,

where ω is the angular velocity of the system.

Other articles related to "moment of inertia matrix, matrix, inertia matrix, moments, inertia, moment of inertia, moment of":

Parallel Axes Rule - Moment of Inertia Matrix - Identities For A Skew-symmetric Matrix
... Let be the skew symmetric matrix associated with the position vector R=(x, y, z), then the product in the inertia matrix becomes This product can be ... the diagonal elements of the outer product matrix, known as its trace ...
True Polar Wander
... In a stable state, the largest moments of inertia axis is aligned with the spin axis, with the smaller two moment of inertia axes lying in the plane of the equator ... rotate as a rigid body to realign the largest moment of inertia axis with the spin axis ...
Rotational Inertia
... Another form of inertia is rotational inertia (→ moment of inertia), which refers to the fact that a rotating rigid body maintains its state of ... Rotational inertia depends on the object remaining structurally intact as a rigid body, and also has practical consequences For example, a gyroscope uses the ...
Stress-strain Index - History and Relation To Moments of Inertia
... information provided by calculating the area moments of inertia and polar moments of inertia ...
List Of Area Moments Of Inertia
... The following is a list of area moments of inertia ... The area moment of inertia or second moment of area has a unit of dimension length4, and should not be confused with the mass moment of inertia ... If the piece is thin, however, the mass moment of inertia equals the areal density times the area moment of inertia ...

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