Editing Euler angles (section)

===Vehicles and moving frames===
{{Main|rigid body}}
{{See also|axes conventions}}

Their main advantage over other orientation descriptions is that they are directly measurable from a gimbal mounted in a vehicle. As gyroscopes keep their rotation axis constant, angles measured in a gyro frame are equivalent to angles measured in the lab frame. Therefore, gyros are used to know the actual orientation of moving spacecraft, and Euler angles are directly measurable. Intrinsic rotation angle cannot be read from a single gimbal, so there has to be more than one gimbal in a spacecraft. Normally there are at least three for redundancy. There is also a relation to the well-known [[gimbal lock]] problem of [[mechanical engineering]].<ref>The relation between the Euler angles and the Cardan suspension is explained in chap. 11.7 of the following textbook: U. Krey, A. Owen, ''Basic Theoretical Physics – A Concise Overview'', New York, London, Berlin, Heidelberg, Springer (2007)&nbsp;.</ref>

When studying rigid bodies in general, one calls the ''xyz'' system ''space coordinates'', and the ''XYZ'' system ''body coordinates''. The space coordinates are treated as unmoving, while the body coordinates are considered embedded in the moving body. Calculations involving [[acceleration]], [[angular acceleration]], [[angular velocity]], [[angular momentum]], and [[kinetic energy]] are often easiest in body coordinates, because then the moment of inertia tensor does not change in time.  If one also diagonalizes the rigid body's moment of inertia tensor (with nine components, six of which are independent), then one has a set of coordinates (called the principal axes) in which the moment of inertia tensor has only three components.

The angular velocity of a rigid body takes a [[Angular velocity#Components from Euler angles|simple form]] using Euler angles in the moving frame. Also the [[Euler's equations (rigid body dynamics)|Euler's rigid body equations]] are simpler because the inertia tensor is constant in that frame.