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By Francis K. Mason

London released WW II - Air

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This is equivalent to the 'gimbal lock' (or nadir) condition which arises with a set of mechanical gimbals when the pitch, or inner, gimbal is rotated through 90°. When 6 approaches H-TT/2, either (f> or \fs may be selected arbitrarily to satisfy some other condition while the unspecified angle is chosen to satisfy eqn. 68). To avoid 'jumps' in the values of 0 or ^ between successive calculations when 0 is in the region of+;r/2, one approach would be to 'freeze' one angle, 0, for instance, at its current value and to calculate ^ in accordance with eqn.

4 Resolution of accelerometer measurements The accelerometers usually provide a measurement of specific force in a body fixed axis set, denoted fb. In order to navigate, it is necessary to resolve the components of the specific force in the chosen reference frame. 6) Superscripts attached to vector quantities denote the axis set in which the vector quantity coordinates are expressed. where Cj5 is a 3 x 3 matrix which defines the attitude of the body frame with respect to the i-frame. 8) This matrix is formed from the elements of the vector G)-J5 = [p q r ] T which represents the turn rate of the body with respect to the i-frame as measured by the gyroscopes.

11 Strapdown inertia! 21) where C£ is the direction cosine matrix used to transform the measured specific force vector into Earth axes. 22) where Q^ is the skew symmetric form of O)J^, the body rate with respect to the Earth-fixed frame. 23) in which Cg = C£T, the transpose of the matrix C£. 12. A variation on this system may be used when it is required to navigate over relatively short distances, with respect to a fixed point on the Earth. A mechanisation of this type may be used for a tactical missile application in which navigation is required with respect to a ground based tracking station.

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