Frames

We need several coordinate frames to express spacecraft attitude dynamics.

ECI (Earth-Centered Inertial) Frame

Inertial frame of our dynamics. Always fixed. Attitude dynamics are usually described based on this frame.

Origin: center of the Earth
X-axis: direction of crossing between the equator and latitude 0 degrees at the initial state
Y-axis: direction of crossing between the equator and longitude +90 degrees at the initial state
Z-axis: direction corresponding to the Earth's rotation axis

ECEF (Earth-Centered Earth-fixed) Frame

Rotating coordinate frame according to the Earth's rotation. This frame is used mainly to express the ground equipment on the Earth.

Origin: center of the Earth
X-axis: longitude 0 degrees on Greenwich meridian
Y-axis: longitude 90 degrees east
Z-axis: direction corresponding to the Earth's north pole

LVLH (Local Vertical Local Horizontal) frame

Referential frame of spacecraft on orbit. This frame describes the motion of spacecraft on orbit. And spacecraft attitude (Spacecraft-fixed frame) is expressed with respect to this frame.

Origin: center of the spacecraft
X-axis: direction of travel on orbit (roll axis)
Y-axis: orthogonal direction to orbit plane (pitch axis)
Z-axis: direction to the Earth (yaw axis)

Body frame (Spacecraft-fixed frame)

Frame that is fixed to the spacecraft body. Describing the attitude of spacecraft.

Origin: center of the spacecraft or referential point on spacecraft
X-axis: X-axis of the spacecraft body
Y-axis: Y-axis of the spacecraft body
Z-axis: Z-axis of the spacecraft body