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gyratio
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There are 7 letters in GYRATIO ( A1G2I1O1R1T1Y4 )
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GYRATIO - In physics, the gyration tensor is a tensor that describes the second moments of position of a collection of particles ...
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In physics, the gyration tensor is a tensor that describes the second moments of position of a collection of particles* * * * * S * * m * n * * * * * * * * = * * * * d * e * f * * * * * * * * * 1 * N * * * * ∑ * * i * = * 1 * * * N * * * * r * * m * * * ( * i * ) * * * * r * * n * * * ( * i * ) * * * * * {\displaystyle S_{mn}\ {\stackrel {\mathrm {def} }{=}}\ {\frac {1}{N}}\sum _{i=1}^{N}r_{m}^{(i)}r_{n}^{(i)}} * where * * * * * r * * m * * * ( * i * ) * * * * * {\displaystyle r_{m}^{(i)}} * is the * * * * * * m * * t * h * * * * * * {\displaystyle \mathrm {m^{th}} } * * Cartesian coordinate of the position vector * * * * * * r * * * ( * i * ) * * * * * {\displaystyle \mathbf {r} ^{(i)}} * of the * * * * * * * i * * t * h * * * * * * {\displaystyle \mathrm {i^{th}} } * particle. The origin of the coordinate system has been chosen such that * * * * * * ∑ * * i * = * 1 * * * N * * * * * r * * * ( * i * ) * * * = * 0 * * * {\displaystyle \sum _{i=1}^{N}\mathbf {r} ^{(i)}=0} * i.e. in the system of the center of mass * * * * * r * * C * M * * * * * {\displaystyle r_{CM}} * . Where * * * * * * r * * C * M * * * = * * * 1 * N * * * * ∑ * * i * = * 1 * * * N * * * * * r * * * ( * i * ) * * * * * {\displaystyle r_{CM}={\frac {1}{N}}\sum _{i=1}^{N}\mathbf {r} ^{(... |