User manual MATLAB AEROSPACE BLOCKSET 3

[. . . ] Aerospace BlocksetTM 3 User's Guide How to Contact The MathWorks Web Newsgroup www. mathworks. com/contact_TS. html Technical Support www. mathworks. com comp. soft-sys. matlab suggest@mathworks. com bugs@mathworks. com doc@mathworks. com service@mathworks. com info@mathworks. com Product enhancement suggestions Bug reports Documentation error reports Order status, license renewals, passcodes Sales, pricing, and general information 508-647-7000 (Phone) 508-647-7001 (Fax) The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 For contact information about worldwide offices, see the MathWorks Web site. Aerospace BlocksetTM User's Guide © COPYRIGHT 2002­2010 by The MathWorks, Inc. The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. [. . . ] 6DoF (Euler Angles) 6DoF (Quaternion) 6DoF ECEF (Quaternion) 6DoF Wind (Quaternion) 6DoF Wind (Wind Angles) 6th Order Point Mass (Coordinated Flight) Custom Variable Mass 6DoF (Euler Angles) Custom Variable Mass 6DoF ECEF (Quaternion) Custom Variable Mass 6DoF Wind (Quaternion) Custom Variable Mass 6DoF Wind (Wind Angles) Simple Variable Mass 6DoF (Euler Angles) 5-170 Custom Variable Mass 6DoF (Quaternion) Simple Variable Mass 6DoF (Quaternion) Simple Variable Mass 6DoF ECEF (Quaternion) Simple Variable Mass 6DoF Wind (Quaternion) Simple Variable Mass 6DoF Wind (Wind Angles) 5-171 Custom Variable Mass 6DoF ECEF (Quaternion) Purpose Implement quaternion representation of six-degrees-of-freedom equations of motion of custom variable mass in Earth-centered Earth-fixed (ECEF) coordinates Equations of Motion/6DoF The Custom Variable Mass 6DoF ECEF (Quaternion) block considers the rotation of a Earth-centered Earth-fixed (ECEF) coordinate frame (XECEF , YECEF , ZECEF ) about an Earth-centered inertial (ECI) reference frame (XECI , YECI , ZECI ). The origin of the ECEF coordinate frame is the center of the Earth, additionally the body of interest is assumed to be rigid, an assumption that eliminates the need to consider the forces acting between individual elements of mass. The representation of the rotation of ECEF frame from ECI frame is simplified to consider only the constant rotation of the ellipsoid Earth (e ) including an initial celestial longitude (LG(0)). This excellent approximation allows the forces due to the Earth's complex motion relative to the "fixed stars" to be neglected. Library Description 5-172 Custom Variable Mass 6DoF ECEF (Quaternion) The translational motion of the ECEF coordinate frame is given below, where the applied forces [Fx Fy Fz]T are in the body frame. Fx Fb = Fy = m Vb + b × Vb + DCMbf e × Vb + DCMbf e × (e × X f ) F z + m Vb + DCMbf (e × X f ) ( ) ( ) ( ) where the change of position in ECEF x f is calculated by x f = DCM fbVb 5-173 Custom Variable Mass 6DoF ECEF (Quaternion) and the velocity of the body with respect to ECEF frame, expressed in body frame (V b) , angular rates of the body with respect to ECI frame, expressed in body frame ( b) . Earth rotation rate ( e) , and relative angular rates of the body with respect to north-east-down (NED) frame, expressed in body frame (rel ) are defined as 0 u p v , = q , = 0 , = + DCM + DCM Vb = rel e b rel bf e be ned e w r l cos VE ( N + h ) ned = - = -VN ( M + h ) -l sin V · tan ( N + h ) E The rotational dynamics of the body defined in body-fixed frame are given below, where the applied moments are [L M N]T, and the inertia tensor I is with respect to the origin O. L Mb = M = I b + b × ( I b ) + Ib N I xx I = - I yx - I zx - I xy I yy - I zy - I xz - I yz I zz The rate of change of the inertia tensor is defined by the following equation. 5-174 Custom Variable Mass 6DoF ECEF (Quaternion) I xx I = - I yx - I zx - I xy I yy - I zy - I xz - I yz I zz The integration of the rate of change of the quaternion vector is given below. 0 b (1) b ( 2 ) b ( 3 ) q0 q0 q 0 -b ( 3 ) b ( 2 ) q1 1 = - 1 -b (1) 2 -b ( 2 ) b ( 3 ) q2 0 -b (1) q2 0 q3 q3 -b ( 3 ) -b ( 2 ) b (1) Dialog Box 5-175 Custom Variable Mass 6DoF ECEF (Quaternion) Units Specifies the input and output units: Units Metric (MKS) Forces Newton Moment Newton meter Foot pound Acceleration Meters per second squared Feet per second squared Feet per second squared Velocity Position Mass Meters per second Feet per second Meters Inertia Kilogram Kilogram meter squared Slug Slug foot squared Slug foot squared English Pound (Velocity in ft/s) English Pound (Velocity in kts) Feet Foot pound Knots Feet Slug 5-176 Custom Variable Mass 6DoF ECEF (Quaternion) Mass type Select the type of mass to use: Fixed Mass is constant throughout the simulation (see 6DoF ECEF (Quaternion)). Mass and inertia vary linearly as a function of mass rate (see Simple Variable Mass 6DoF ECEF (Quaternion)). Mass and inertia variations are customizable. Simple Variable Custom Variable The Simple Variable selection conforms to the previously described equations of motion. Initial position in geodetic latitude, longitude and altitude The three-element vector for the initial location of the body in the geodetic reference frame. Initial velocity in body-axis The three-element vector containing the initial velocity of the body with respect to ECEF frame, expressed in body frame. Initial Euler orientation The three-element vector containing the initial Euler rotation angles [roll, pitch, yaw], in radians. Euler rotation angles are those between the body and north-east-down (NED) coordinate systems. Initial body rotation rates The three-element vector for the initial angular rates of the body with respect to NED frame, expressed in body frame, in radians per second. Planet model Specifies the planet model to use, Custom or Earth (WGS84). 5-177 Custom Variable Mass 6DoF ECEF (Quaternion) Flattening Specifies the flattening of the planet. This option is only available when Planet model is set to Custom. Equatorial radius of planet Specifies the radius of the planet at its equator. The units of the equatorial radius parameter should be the same as the units for ECEF position. This option is only available when Planet model is set to Custom. Rotational rate Specifies the scalar rotational rate of the planet in rad/s. This option is only available when Planet model is set to Custom. Celestial longitude of Greenwich source Specifies the source of Greenwich meridian's initial celestial longitude: Internal External Use celestial longitude value from mask dialog. Use external input for celestial longitude value. Celestial longitude of Greenwich The initial angle between Greenwich meridian and the x-axis of the ECI frame. Inputs and Outputs Input First Second Third Fourth Dimension Type Vector Vector Scalar Scalar Description Contains the three applied forces in body-fixed axes. Contains the three applied moments in body-fixed axes. [. . . ] Contains the total intensity in selected units. Limitations The WMM2010 specification produces data that is reliable five years after the epoch of the model, which is January 1, 2015. 5-568 World Magnetic Model 2010 The internal calculation of decimal year does not take into account local time or leap seconds. The WMM2010 specification describes only the long-wavelength spatial magnetic fluctuations due to the Earth's core. Intermediate and short-wavelength fluctuations, contributed from the crustal field (the mantle and crust), are not included. Also, the substantial fluctuations of the geomagnetic field, which occur constantly during magnetic storms and almost constantly in the disturbance field (auroral zones), are not included. Reference See Also http://www. ngdc. noaa. gov/geomag/WMM/DoDWMM. shtml World Magnetic Model 2000, World Magnetic Model 2005 5-569 Zonal Harmonic Gravity Model Purpose Library Description Calculate zonal harmonic representation of planetary gravity Environment/Gravity The Zonal Harmonic Gravity Model block calculates the zonal harmonic representation of planetary gravity at a specific location based on planetary gravitational potential. [. . . ]