  In the presence of Earth gravity and gravity-gradient forces, centrifugal and
Coriolis forces caused by the Earth rotation, the phase of the time-domain atom
interferometers is calculated with accuracy up to the terms proportional to the
fourth degree of the time separation between pulses. We considered double-loop
atom interferometers and found appropriate condition to eliminate their
sensitivity to acceleration to get atomic gyroscope, or to eliminate the
sensitivity to rotation to increase accuracy of the atomic gravimeter.
Consequent use of these interferometers allows one to measure all components of
the acceleration and rotation frequency projection on the plane perpendicular
to gravity acceleration. Atom interference on the Raman transition driving by
noncounterpropagating optical fields is proposed to exclude stimulated echo
processes which can affect the accuracy of the atomic gyroscopes. Using
noncounterpropagating optical fields allows one to get a new type of the Ramsey
fringes arising in the unidirectional Raman pulses and therefore centered at
the two-quantum line center. Density matrix in the Wigner representation is
used to perform calculations. It is shown that in the time between pulses, in
the noninertial frame, for atoms with fully quantized spatial degrees of
freedom, this density matrix obeys classical Liouville equations.
