drdazl_c |

Table of contents## Proceduredrdazl_c ( Derivative of rectangular w.r.t. AZ/EL ) void drdazl_c ( SpiceDouble range, SpiceDouble az, SpiceDouble el, SpiceBoolean azccw, SpiceBoolean elplsz, SpiceDouble jacobi [3][3] ) ## AbstractCompute the Jacobian matrix of the transformation from azimuth/elevation to rectangular coordinates. ## Required_ReadingNone. ## KeywordsCOORDINATES DERIVATIVES MATRIX ## Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- range I Distance of a point from the origin. az I Azimuth of input point in radians. el I Elevation of input point in radians. azccw I Flag indicating how azimuth is measured. elplsz I Flag indicating how elevation is measured. jacobi O Matrix of partial derivatives. ## Detailed_Inputrange is the distance from the origin of the input point specified by `range', `az', and `el'. Negative values for `range' are not allowed. Units are arbitrary and are considered to match those of the rectangular coordinate system associated with the output matrix `jacobi'. az is the azimuth of the point. This is the angle between the projection onto the XY plane of the vector from the origin to the point and the +X axis of the reference frame. `az' is zero at the +X axis. The way azimuth is measured depends on the value of the logical flag `azccw'. See the description of the argument `azccw' for details. The range (i.e., the set of allowed values) of `az' is unrestricted. See the -Exceptions section for a discussion on the `az' range. Units are radians. el is the elevation of the point. This is the angle between the vector from the origin to the point and the XY plane. `el' is zero at the XY plane. The way elevation is measured depends on the value of the logical flag `elplsz'. See the description of the argument `elplsz' for details. The range (i.e., the set of allowed values) of `el' is [-pi/2, pi/2], but no error checking is done to ensure that `el' is within this range. See the -Exceptions section for a discussion on the `el' range. Units are radians. azccw is a flag indicating how the azimuth is measured. If `azccw' is SPICETRUE, the azimuth increases in the counterclockwise direction; otherwise `az' increases in the clockwise direction. elplsz if a flag indicating how the elevation is measured. If `elplsz' is SPICETRUE, the elevation increases from the XY plane toward +Z; otherwise toward -Z. ## Detailed_Outputjacobi is the matrix of partial derivatives of the transformation from azimuth/elevation to rectangular coordinates. It has the form .- -. | dx/drange dx/daz dx/del | | | | dy/drange dy/daz dy/del | | | | dz/drange dz/daz dz/del | `- -' evaluated at the input values of `range', `az' and `el'. `x', `y', and `z' are given by the familiar formulae x = range * cos( az ) * cos( el ) y = range * sin( azsnse * az ) * cos( el ) z = range * sin( eldir * el ) where `azsnse' is +1 when `azccw' is SPICETRUE and -1 otherwise, and `eldir' is +1 when `elplsz' is SPICETRUE and -1 otherwise. ## ParametersNone. ## Exceptions1) If the value of the input parameter `range' is negative, the error SPICE(VALUEOUTOFRANGE) is signaled by a routine in the call tree of this routine. 2) If the value of the input argument `el' is outside the range [-pi/2, pi/2], the results may not be as expected. 3) If the value of the input argument `az' is outside the range [0, 2*pi], the value will be mapped to a value inside the range that differs from the input value by an integer multiple of 2*pi. ## FilesNone. ## ParticularsIt is often convenient to describe the motion of an object in azimuth/elevation coordinates. It is also convenient to manipulate vectors associated with the object in rectangular coordinates. The transformation of an azimuth/elevation state into an equivalent rectangular state makes use of the Jacobian matrix of the transformation between the two systems. Given a state in latitudinal coordinates, ( r, az, el, dr, daz, del ) the velocity in rectangular coordinates is given by the matrix equation t | t (dx, dy, dz) = jacobi| * (dr, daz, del) |(r,az,el) This routine computes the matrix | jacobi| |(r,az,el) In the azimuth/elevation coordinate system, several conventions exist on how azimuth and elevation are measured. Using the `azccw' and `elplsz' flags, users indicate which conventions shall be used. See the descriptions of these input arguments for details. ## ExamplesThe numerical results shown for this example may differ across platforms. The results depend on the SPICE kernels used as input, the compiler and supporting libraries, and the machine specific arithmetic implementation. 1) Find the azimuth/elevation state of Venus as seen from the DSS-14 station at a given epoch. Map this state back to rectangular coordinates as a check. Task description ================ In this example, we will obtain the apparent state of Venus as seen from the DSS-14 station in the DSS-14 topocentric reference frame. We will use a station frames kernel and transform the resulting rectangular coordinates to azimuth, elevation and range and its derivatives using recazl_c and dazldr_c. We will map this state back to rectangular coordinates using azlrec_c and ## RestrictionsNone. ## Literature_ReferencesNone. ## Author_and_InstitutionJ. Diaz del Rio (ODC Space) ## Version-CSPICE Version 1.0.0, 30-DEC-2021 (JDR) ## Index_EntriesJacobian matrix of rectangular w.r.t. AZ/EL coordinates range, azimuth and elevation to rectangular derivative Range, AZ and EL to rectangular velocity conversion |

Fri Dec 31 18:41:04 2021