# Parallel Axes Rule - in Classical Mechanics

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 Jij from an inertia tensor about a centre of mass Iij when the pivot point is a displacement a from the centre of mass:

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

$mathbf{I}^{mathrm{displaced}} = mathbf{I}^{mathrm{center}} + m left " src="http://upload.wikimedia.org/math/5/6/8/5685f05491ff00428551ec8ad91b5de0.png" />

where m is the total mass of the rigid body, E3 is the 3 × 3 identity matrix, and is the outer product.

### Other articles related to "classical, in classical mechanics, in classical":

Natural Killer Cell - NK Cell Receptors - Activating Receptors
... presence in mice, while humans have only one pseudogenic Ly49 the receptor for classical (polymorphic) MHC I molecules ... family receptor, conserved in both rodents and primates and identifies non-classical (also non-polymorphic) MHC I molecules like HLA-E ... of nonamer peptide epitope derived from the signal sequence of classical MHC class I molecules, which is generated by the sequential action of signal peptide peptidase and the proteasome ...
Canonical Coordinates - Definition, in Classical Mechanics
... In classical mechanics, canonical coordinates are coordinates and in phase space that are used in the Hamiltonian formalism ...
Kishori Amonkar
... आमोणकर) (born 10 April 1931) is an Indian singer who performs in the classical genre khyal and the light classical genres thumri and bhajan ... Amonkar trained under her mother, classical singer Mogubai Kurdikar of the Jaipur gharana (musical tradition of Jaipur), but experimented with a variety of vocal styles in her career ... of the preeminent representatives of Hindustani classical music ...
Cor Anglais - Use Outside Classical Music
... Though primarily featured in classical music, the cor anglais has also been used by a few musicians as a jazz instrument most prominent among these are Paul McCandless, Jean-Luc Fillon, Sonny ... quadruple and sextuple reeds does not include bagpipes) European classical (modern) Piccolo oboe Piccolo heckelphone Oboe Oboe d'amore Cor anglais (English horn ...
Foot (prosody) - The Poetic Feet in Classical Meter
... Below are listed the names given to the poetic feet by classical metrics ... secondarily by the pattern of vowel lengths (in classical languages) or syllable stresses (in English poetry) which they comprise ... The following lists describe the feet in terms of vowel length (as in classical languages) ...

### 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)