Gyration tensor

In physics, the gyration tensor is a tensor that describes the second moments of position of a collection of particles In physics, the gyration tensor is a tensor that describes the second moments of position of a collection of particles 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.e. in the system of the center of mass r C M {displaystyle r_{CM}} . Where