# Dielectric barrier discharge

## List of 3D inertia tensors

This list of moment of inertia tensors is given for principal axes of each object.

Description Figure Moment of inertia tensor
Solid sphere of radius r and mass m ${\displaystyle I={\begin{bmatrix}{\frac {2}{5}}mr^{2}&0&0\\0&{\frac {2}{5}}mr^{2}&0\\0&0&{\frac {2}{5}}mr^{2}\end{bmatrix}}}$
Hollow sphere of radius r and mass m
Solid ellipsoid of semi-axes a, b, c and mass m ${\displaystyle I={\begin{bmatrix}{\frac {1}{5}}m(b^{2}+c^{2})&0&0\\0&{\frac {1}{5}}m(a^{2}+c^{2})&0\\0&0&{\frac {1}{5}}m(a^{2}+b^{2})\end{bmatrix}}}$
Right circular cone with radius r, height h and mass m, about the apex ${\displaystyle I={\begin{bmatrix}{\frac {3}{5}}mh^{2}+{\frac {3}{20}}mr^{2}&0&0\\0&{\frac {3}{5}}mh^{2}+{\frac {3}{20}}mr^{2}&0\\0&0&{\frac {3}{10}}mr^{2}\end{bmatrix}}}$
Solid cuboid of width w, height h, depth d, and mass m ${\displaystyle I={\begin{bmatrix}{\frac {1}{12}}m(h^{2}+d^{2})&0&0\\0&{\frac {1}{12}}m(w^{2}+d^{2})&0\\0&0&{\frac {1}{12}}m(w^{2}+h^{2})\end{bmatrix}}}$
Slender rod along y-axis of length l and mass m about end
Slender rod along y-axis of length l and mass m about center
Solid cylinder of radius r, height h and mass m
Thick-walled cylindrical tube with open ends, of inner radius r1, outer radius r2, length h and mass m