# Method of autonomous measurement of angular speed vector

FIELD: measurement technology.

SUBSTANCE: method can be used in moving objects' spatial orientation systems. Before beginning of movement of object, the coordinate system is chosen being comfortable for observer. Three stars are selected, along directions of which stars the speeds have to be measured and their angular coordinates are measured. After movement starts, current values of linear velocity are measured on the base of directions of navigating stars. Changes in linear velocity are calculated from directions of navigating stars, which are changes are caused by rotation of object, and basic components of angular speed vector are determined from directions of navigating stars.

EFFECT: improved precision of measurement.

The invention relates to techniques for Autonomous measurement of the angular velocity vector of a moving object. It can be used in various fields of science and technology, mainly in systems of Autonomous control and navigation of spacecraft, aircraft, missiles.

The way the Autonomous measurement of the angular velocity vector based on the measurement of changes in the linear velocity of a moving object in the directions of the 3 selected stars, obtained with the help of gauges made from the center of rotation of the object.

Existing methods of measuring angular velocity based on the measurement of deviations from the reference directions that are generated, for example, the axes of the gyroscope or the directions on external objects.

Because the physical basis for, the proposed method has no prototype is closest in technical essence equivalent.

The proposed method has high accuracy, high sensitivity detection of unauthorized games, solves the problem of measuring angular velocity with the same equipment, and methods of Autonomous dimension of the vector of linear speed (patent No. 2227302, the invention application, registration No. 2004117733) and the way spatial orientation and stabilization, the application for invention No. 2004134757/28(037811). The movement of the meter when the rotation amount is that causes a change in the measured linear velocity in the direction of the observed stars. This change in uniform rotation of an object is sinusoidal with amplitude and phase determined by the coordinates of the point of location of the receiver on the object. The oscillation frequency of the sinusoid is proportional to the angular velocity of rotation of the object.

In the General case, the angular velocity of a rigid body is the vector ωnumerically equal to the first derivative of the angle ϕ time

and directed along the axis of rotation so that from his end of the rotation of the body could be seen happening in a counterclockwise direction.

The projection of the vector ω direction 3 is taken to measure the stars (hereinafter - the navigation stars) are defined as follows:

Here ν - the linear velocity of the receiver in the direction of the navigation stars, due to the rotation of the object

t_{and}- the time interval between two adjacent measurement speed

d - distance between the receiver and the center of rotation of the object.

Almost always the condition νt_{and}≪d, therefore, true equality tgϕ=ϕ,

Measuring the linear velocity in the directions of the navigation stars determine the total rate resulting from the "target" speed motion the object sweeps ν
_{tr}and speed caused by the rotation ν. Due to the fact that ν_{tr}known and predictable, the speed caused by the rotation of an object, defined as

ν=ν_{and}-ν_{tr},

where ν_{and}- measured speed.

Changes in the linear velocity in the directions respectively the 1st, 2nd and 3rd navigational stars, caused by the rotation of an object, defined as

where,,- measured speed in the directions respectively the 1st, 2nd and 3rd navigational stars,

,,- planned trajectory velocity along the same lines.

The criterion for detecting rotation of an object is the excess value ν threshold ν≥ν_{p}. Here ν_{p}- threshold value changes the linear velocity determined from the conditions of flight.

At the location of the receivers, tracking navigational stars, at one point on the object or at a close distance from each other so that the errors introduced by their spatial separation can be neglected, and simultaneous measurement in all three dimensions of the projection of the vector ω at the direction of the stars are determined by the formulas the mi

In the General case, when placing the measuring velocities in the directions of the navigation star in arbitrary points on the object may note the readings of the meters to one point by calculating the amendments. However, the mathematical apparatus of such a calculation is relatively bulky, so to simplify the presentation only covers accommodation measures at small distances from each other, does not significantly affect the accuracy of the vector ω, as mentioned above. The more that this accommodation option receivers technical feasibility and for many reasons preferable.

Projected vector ω at the direction of the stars determine the end of this vector in the global rectangular coordinate system (rectangular coordinate system) as the intersection of three planes passing through the ends of the projections perpendicular to the directions on the stars. The coordinate system origin is at the point of the beginning of the movement (start). If necessary, use "object" frame by moving the origin to the point of location of a moving object.

The system of equations intersecting planes is

The projection of the vector ω on the axis of the rectangular coordinate system is determined by the formula

• - vascular systems of equations intersecting planes,

a α_{1}that β_{1}that γ_{1}; α_{2}that β_{2}that γ_{2}; α_{3}that β_{3}that γ_{3}angular coordinates respectively the 1st, 2nd and 3rd navigational stars in the global rectangular coordinate system, measured or selected directory.

The unit of the angular velocity vector is determined by the formula

and the direction cosines of the vector of angular velocity according to the formula

The objective of the invention is resolved.

When carrying out the invention performs the following steps :

Before the start of the movement (start):

- choose a coordinate system convenient for the user (below, as already mentioned, the presentation is applied to a rectangular coordinate system with the origin at the starting point);

- choose the three stars in the directions which will be measured speed; one of the coordinate axes may be aligned with the direction on one of the stars, the other two stars chosen closer to the other coordinate axes;

- measured (or determined by the directory) elevation the s coordinates of the selected stars at the time of launch;

- take radiation selected stars;

- carry out maintenance of the stars over the angular coordinates;

- record the start time and the geographical coordinates of the starting point (if necessary for these data is determined by the initial velocity of the object relative to the world space equal to the velocity of the point at the beginning of the movement).

After starting (start):

- measure the current values of the linear velocities in the directions of the navigation stars;

- calculated by formulas (2) changes in the linear velocity in the directions of the navigation stars, caused by the rotation of an object ν_{1}that ν_{2}that ν_{3};

determine the projection of the angular velocity vector in the directions of the navigation star in the formulas (3);

determine the projection of the angular velocity vector of the object on the axis of a rectangular system of coordinates by the formulas (4);

- determine the unit rate and direction cosines of the angular velocity vector by the formulas (5) and (6) respectively.

The ability of the method and the goal of the invention is determined by the achievable accuracy of measurement of the linear velocity of the object in the directions of the navigation stars, the accuracy of determining the angular coordinates of the stars before the start of the movement (start) of the object and its angular support during the movement, the possibility of computing what about the formulas (1)to(6). Measurement error of the angular coordinates of the stars prior to the movement of astronomical instruments be fractions of seconds of arc. Their influence on the accuracy of determining the angular velocity of the object, as the effect of errors in the tracking of the stars over the angular coordinates, errors introduced by the calculations can be neglected due to their smallness. With this in mind, the measurement error vector ω is defined as the differential is found from the formula (1)

The linear speed of the object can be determined according to the method set forth in patent No. 2227302, or by the method described in the patent application, registration No. 2004117733. Through these methods, the measurement error of the linear velocity, and hence changes in speed caused by the rotation of the object is 3(10^{-3}-10^{-4}) m/S. When the value of the ejection velocity meters from the center of rotation, for example by three meters, the accuracy of the measurement of angular velocity the invention is δω=(10^{-3}÷10^{-4}) radian/c or 5.7(10^{-2}÷10^{-3}) C/c.

The invention is now realizable and provides high precision measurement of the angular velocity vector of a moving object, not time-dependent and range.

The way the Autonomous measurement of the angular velocity vector of a moving object, what about the radiation of the stars, characterized in that prior to the movement choose three stars, measured or determined by the directory, their coordinates, taking radiation mentioned stars, record the time and the coordinates of the starting point of the movement, and after the start of movement of the measured values of the linear velocity in the directions of the stars, calculate the change of linear velocity along these lines, caused by the rotation of an object according to the formula

where,,- measured speed in the directions respectively the 1st, 2nd and 3rd navigational stars;

,,- planned trajectory velocity along the lines of,

determine the projection of the angular velocity vector in the direction of the stars by the formula

where d is the distance between the receiver and the center of rotation of the object

determine the projection of the angular velocity vector on the axis of a rectangular system of coordinates according to the formula

- vascular systems of equations intersecting planes,

a α_{1}that β_{1}that γ_{1}; α_{2}that β_{2}that γ_{2}; α_{3}that β_{3}that γ_{3}angular coordinates respectively the 1st, 2nd and 3rd of the navigation star in the global rectangular coordinate system, specify the module and direction cosines of the vector of angular velocity according to the formula

where α_{ω}that β_{ω}that γ_{ω}the angles between the angular velocity vector and the axes of the global rectangular coordinate system.

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