**In Classical Mechanics**

In classical mechanics, the Parallel axis theorem (also known as Huygens-Steiner theorem) can be generalized to calculate a new inertia tensor * J_{ij}* from an inertia tensor about a centre of mass

*when the pivot point is a displacement*

**I**_{ij}*from the centre of mass:*

**a**where

is the displacement vector from the centre of mass to the new axis, and

is the Kronecker delta.

We can see that, for diagonal elements (when *i* = *j*), displacements perpendicular to the axis of rotation results in the above simplified version of the parallel axis theorem.

This can also be formulated as follows. Once the moment of inertia tensor has been calculated for rotations about the center of mass of the rigid body, there is a useful labor-saving method to compute the tensor for rotations offset from the center of mass.

If the axis of rotation is displaced by a vector **R** from the center of mass, the new moment of inertia tensor equals

- center}} + m left " src="http://upload.wikimedia.org/math/5/6/8/5685f05491ff00428551ec8ad91b5de0.png" />

where *m* is the total mass of the rigid body, **E**_{3} is the 3 × 3 identity matrix, and is the outer product.

Read more about this topic: Parallel Axes Rule

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### Famous quotes containing the words mechanics and/or classical:

“It is only the impossible that is possible for God. He has given over the possible to the *mechanics* of matter and the autonomy of his creatures.”

—Simone Weil (1909–1943)

“Compare the history of the novel to that of rock ‘n’ roll. Both started out a minority taste, became a mass taste, and then splintered into several subgenres. Both have been the typical cultural expressions of classes and epochs. Both started out aggressively fighting for their share of attention, novels attacking the drama, the tract, and the poem, rock attacking jazz and pop and rolling over *classical* music.”

—W. T. Lhamon, U.S. educator, critic. “Material Differences,” Deliberate Speed: The Origins of a Cultural Style in the American 1950s, Smithsonian (1990)