Triaxial

Triaxial describes objects or systems that involve three axes or three directions in space. The term derives from Latin tri- meaning three and axia meaning axis. It is used in geometry, mechanics, astronomy, and sensor technology.

In geometry, a triaxial ellipsoid has three mutually perpendicular axes of different lengths (a, b, c). Its equation is x^2/a^2 + y^2/b^2 + z^2/c^2 = 1 with a, b, c all distinct. This distinguishes it from a spheroid, which has two equal axes, or a sphere, which has all three equal.

In mechanics and material science, a triaxial state of stress involves three independent principal stresses acting along three perpendicular directions. It is common in soil and rock mechanics and is studied using triaxial testing, which applies confinement pressure and axial load to samples to simulate underground conditions.

In astronomy and astrophysics, triaxial describes systems with three unequal principal axes, such as triaxial galaxies or dark matter halos, leading to non-axisymmetric shapes and dynamics. In sensor technology, a triaxial device measures along three perpendicular axes, as in triaxial accelerometers and magnetometers, enabling three-dimensional motion or field sensing.