**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 P_{i}, i=1,...,n be located at the coordinates **r**_{i} and velocities **v**_{i}. Select a reference point **R** and compute the relative position and velocity vectors,

where ω is the angular velocity of the system.

Read more about this topic: Moment Of Inertia

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

**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

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**matrix**, known as its trace ...

... 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 ...

... 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 ...

... information provided by calculating the area

**moments**of

**inertia**and polar

**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

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“As all historians know, the past is a great darkness, and filled with echoes. Voices may reach us from it; but what they say to us is imbued with the obscurity of the *matrix* out of which they come; and try as we may, we cannot always decipher them precisely in the clearer light of our day.”

—Margaret Atwood (b. 1939)

“Fashion, by which what is really fantastic becomes for a *moment* the universal.”

—Oscar Wilde (1854–1900)

“What is wrong with priests and popes is that instead of being apostles and saints, they are nothing but empirics who say “I know” instead of “I am learning,” and pray for credulity and *inertia* as wise men pray for scepticism and activity.”

—George Bernard Shaw (1856–1950)