Bodyfixed

Body-fixed frame, or body frame, is a reference frame attached to a rigid body such that its origin is fixed to the body and its axes rotate with the body. The origin is commonly located at the center of mass, so the frame moves and rotates together with the body.

In dynamics and control, quantities are often expressed in the body-fixed frame for convenience, such as velocity components or forces along the body axes. Attitude is the orientation of the body-fixed frame relative to an inertial frame. Orientation is described by a rotation from the body frame to the space frame, denoted R_b^I, mapping body-frame coordinates to inertial-frame coordinates.

Transformations between frames use rotation matrices, Euler angles, or quaternions. The body angular velocity omega relates to the time derivative of the orientation via dot{R} = R [omega]_x, where [omega]_x is the skew-symmetric matrix corresponding to omega. This formalism allows concise description of the body’s rotational dynamics and its interaction with external torques.

Common applications include spacecraft attitude control, aircraft flight dynamics, mobile robotics, and biomechanics. In these fields, measurements from sensors such as gyroscopes or accelerometers are often interpreted in the body-fixed frame, while navigation and guidance algorithms may operate in an inertial frame, requiring frame-to-frame transformations.

See also: inertial frame, space-fixed frame, rotation matrix, quaternion, Euler angles, rigid body dynamics.