An Integrated, Modular Simulation System for Education ... - Cal Poly

each of the linear force terms. The body axis accelerations are integrated to body axisvelocities and rates. Table 6 shows how the body axis velocities are then combined withthe previous Euler angles to obtain the world axis velocities (Table 6) (u out the nose, vTable 6 Euler velocity Equations∂X/∂t = ucosΘcosΨ + v(sinΦsinΘcosΨ - cosΦsinΨ) + w(cosΦsinΘcosΨ+sinΦsinΨ)∂Y/∂t = ucosΘsinΨ + v(sinΦsinΘsinΨ+cosΦcosΨ)+w(cosΦsinΘsinΨ-sinΦcosΨ)∂Z/∂t = usinΘ + vsinΦcosΘ+wcosΦcosΘTable 7 Euler Rate Equations∂Φ/∂t = p+(qsinΦ+ rcosΦ)tanΘ∂Θ/∂t = qcosΦ - rsinΦ∂Ψ/∂t = (qsinΦ + rcosΦ)secΘout the right wing, w down). The world axis velocities are integrated to obtain the currentposition in the world (flat earth — X North, Y East, Z toward the center of the earth)coordinate axis. Table 7 shows how the body axis rates (p about the long axis, q about thewing axis, r about the vehicle vertical axis) are combined with the previous Euler anglesto obtain the Euler rates. The Euler rates are integrated to obtain the current Euler anglesΨ - yaw (positive east and 0 degrees north), Θ - pitch (positive up and 0 degrees levelfrom the horizon - flat earth), Φ - roll (positive right wing down, 0 degrees no roll).Finally the angles are reduced to remain in the first multiple of pi.The model was originally created and tested as a Matlab m file program(FASAND) to demonstrate the coding of 6 DOF equations of motion in a genericprogramming language. The code is functional, however, on a PC the rate of integrationlimits the usefulness as a research tool. The version intended to be used for batchsimulations is the Simulink S-function. In addition to the basic equations of motion theFASAND code includes the wind2body transform function and the Euler and RK432