In order to be a tensor, a quantity needs to be a linear function. It also needs to change, according to certain rules, in response to a change of frame.
Geometry Tensors
Projection Tensor
| Pe = |
|
|
= |
| cos2α |
sin α cos α |
| sin α cos α |
sin2 α |
|
Rotation Tensor
Reflection Tensor
Mechanics Tensors
Inertial Moment Tensor
This relates the torque bivector to the angular acceleration bivector of a solid body. This is a property of the solid body. In three dimensions it is defined by a 3×3 matrix, the components of it depends on its shape and in particular its mass distribution, however the way that these components vary with a change in reference frame is a tensor property.
| I = |
∫ r2 dm = |
| Ix |
-Pxy |
-Pxz |
| -Pxy |
Iy |
-Pyz |
| -Pxz |
-Pyz |
Iz |
|
The Inertia Tensor in 'n' dimensions is discussed on this page.
Stress Tensor
Strain Tensor
Elastic Tensor
