214
4 Navigations from Ground to Space
can work normally in any medium environment such as underwater, mine pit, tunnel,
Earth surface, near-earth space and outer space and provides complete navigation
information such as three-dimensional position, velocity and attitude of the movable
object in all-weather and continual manner, with high data update rate and good
stability. All of the advantages about the INS are incomparable to other navigation
system, so that the INS has extremely important engineering application value and
strategic research significance. However, because there are the drifts for the IMU,
the inertial navigation error is gradually accumulated over time, and generally the
INS cannot be used independently for a long time. In addition, the initial alignment
time needed is long for the alone INS, and to develop high-precision IMU is difficult
in technique, with a high cost and an expensive price.
4.4.2 Development and Application
The Swiss mathematician and physicist, Leonhard Euler (1707−1783), spent most
of his life in Russia and Germany and was the academician professor at the Saint
Petersburg Academy of Science in Russia. He not only made decisive and formative
contributions to the subjects of geometry, calculus, mechanics and number theory,
but also developed methods for solving problems in observational astronomy and
demonstrated useful applications of mathematics in technology and public affairs.
In 1765, L. Euler first used analytical method to explain the essential problem
of fixed-point rotation of rigid body, and created the fundamental theory of rotor
gyroscope mechanics. The Franco-Italian mathematician and astronomer, JosephLouis Lagrange (1736−1813), made significant contributions to the field of analysis,
number theory, and both classical and celestial mechanics. In 1778, he proposed the
differential equations of motion of a rigid body rotating at a fixed point under the
action of gravitational moment. In 1851, a French physicist Jean Foucault proved
that the Earth rotates about its axis, by interpreting the motion of a heavy iron ball
swinging from a wire of 67 m long, which was well known as “Foucault pendulum”.
The pendulum always swung in the vertical plane, but on a rotating Earth, this vertical
plane slowly changed at a rate and direction dependent on the geographic latitude of
its location. For this demonstration, the gyroscope was invented by Foucault as part of
a two-pronged investigation into the rotation of the Earth. In the 1880s, the technology
of using motor to drive gyro rotor appeared to improve the stability of the gyro rotor
rotation, and the device for testing the gyrocompass that is a type of non-magnetic
compass based on a fast-spinning disk and the rotation of the Earth to automatically
find geographical direction was developed. In 1908, Hermann Anschütz-Kaempfe,
a German inventor, designed a single-rotor-swinging gyrocompass, which can automatically find the North based on the gravitational moment, solving the problem
of long-distance navigation of ships and submarine. Soon afterward, an American
inventor Elmer A. Sperry built the first automatic pilot using a gyroscope to maintain
an aircraft on course. In 1923, a German engineer Maximilian Schuler pointed out
that if the gyrocompass was tuned to have an 84.4-min period of oscillation then it
4 Navigations from Ground to Space
can work normally in any medium environment such as underwater, mine pit, tunnel,
Earth surface, near-earth space and outer space and provides complete navigation
information such as three-dimensional position, velocity and attitude of the movable
object in all-weather and continual manner, with high data update rate and good
stability. All of the advantages about the INS are incomparable to other navigation
system, so that the INS has extremely important engineering application value and
strategic research significance. However, because there are the drifts for the IMU,
the inertial navigation error is gradually accumulated over time, and generally the
INS cannot be used independently for a long time. In addition, the initial alignment
time needed is long for the alone INS, and to develop high-precision IMU is difficult
in technique, with a high cost and an expensive price.
4.4.2 Development and Application
The Swiss mathematician and physicist, Leonhard Euler (1707−1783), spent most
of his life in Russia and Germany and was the academician professor at the Saint
Petersburg Academy of Science in Russia. He not only made decisive and formative
contributions to the subjects of geometry, calculus, mechanics and number theory,
but also developed methods for solving problems in observational astronomy and
demonstrated useful applications of mathematics in technology and public affairs.
In 1765, L. Euler first used analytical method to explain the essential problem
of fixed-point rotation of rigid body, and created the fundamental theory of rotor
gyroscope mechanics. The Franco-Italian mathematician and astronomer, JosephLouis Lagrange (1736−1813), made significant contributions to the field of analysis,
number theory, and both classical and celestial mechanics. In 1778, he proposed the
differential equations of motion of a rigid body rotating at a fixed point under the
action of gravitational moment. In 1851, a French physicist Jean Foucault proved
that the Earth rotates about its axis, by interpreting the motion of a heavy iron ball
swinging from a wire of 67 m long, which was well known as “Foucault pendulum”.
The pendulum always swung in the vertical plane, but on a rotating Earth, this vertical
plane slowly changed at a rate and direction dependent on the geographic latitude of
its location. For this demonstration, the gyroscope was invented by Foucault as part of
a two-pronged investigation into the rotation of the Earth. In the 1880s, the technology
of using motor to drive gyro rotor appeared to improve the stability of the gyro rotor
rotation, and the device for testing the gyrocompass that is a type of non-magnetic
compass based on a fast-spinning disk and the rotation of the Earth to automatically
find geographical direction was developed. In 1908, Hermann Anschütz-Kaempfe,
a German inventor, designed a single-rotor-swinging gyrocompass, which can automatically find the North based on the gravitational moment, solving the problem
of long-distance navigation of ships and submarine. Soon afterward, an American
inventor Elmer A. Sperry built the first automatic pilot using a gyroscope to maintain
an aircraft on course. In 1923, a German engineer Maximilian Schuler pointed out
that if the gyrocompass was tuned to have an 84.4-min period of oscillation then it