What is a frame?
A frame of reference is a co-ordinate system with respect to which we make observations.
An inertial frame of reference is one in which Newton's laws of motion are valid. A frame of reference which moves at a constant velocity with respect to an inertial frame is also inertial.
There exist non inertial frames also, in which we need to account for pseudo forces in order to apply Newton’s laws. Non inertial frames are accelerating frames.
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Earth Centered Inertial Frame (ECIF)
The origin is fixed to the center of the Earth. The x-axis points in the direction of vernal equinox, z axis is along axis of rotation of earth, and y axis completes the right handed co-ordinate system. It is assumed to be an inertial frame, though it is actually in circular motion hence an accelerating frame.
Earth Centered Earth Fixed (ECEF) Frame
The origin is fixed to the center of the Earth. The x axis points toward intersection of prime meridian and equator, z axis is along the axis of rotation of earth and y axis completes the right handed co-ordinate system. It is a rotating frame, hence a non-inertial frame. It is useful when co-ordinates of any body are to be described
Orbital Frame
Orbital frame is used when the orbit of a body around another body is assumed to be circular. The origin is fixed to the orbiting body. The x axis points in the direction of velocity of velocity of orbiting body, z axis is directed from the orbiting body to the center of the body around which it orbits, and the y axis completes the right handed co-ordinate system (thus forming normal vector to the orbital plane). It is a rotating frame hence a non-inertial frame.
Body Frame
It is fixed to the body which is being analyzed. The axis can be oriented arbitrarily, but are generally chosen to be the principal axes of inertia. The body (to which the body frame is fixed) as observed with respect to the body frame is stationary. It may be an inertial or non inertial frame depending on the motion of the body.
For illustrations, visit http://www.dept.aoe.vt.edu/~cdhall/courses/aoe4140/refframes.pdf.
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