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| # -*- coding: utf-8 -*- | |
| """ | |
| The axes are denoted: | |
| 1: Earth | |
| 2: Body | |
| 3: Zero side slip - rotation around z, to apply roll | |
| 4: Wind axes - to replicate the CFD condition with wind coming straight onto the body | |
| In Crowther & Potts, z-axis is defined pointing downwards. Here, it points upwards | |
| leading to some different signs. | |
| """ | |
| import numpy as np | |
| from numpy import cos,sin,matmul | |
| def T_12(attitude): | |
| """ | |
| Transform from Earth axes to Body axes | |
| """ | |
| phi, theta, psi = attitude | |
| return np.array([[cos(theta)*cos(psi), sin(phi)*sin(theta)*cos(psi) - cos(phi)*sin(psi), cos(phi)*sin(theta)*cos(psi) + sin(phi)*sin(psi)], | |
| [cos(theta)*sin(psi), sin(phi)*sin(theta)*sin(psi) + cos(phi)*cos(psi), cos(phi)*sin(theta)*sin(psi) - sin(phi)*cos(psi)], | |
| [-sin(theta), sin(phi)*cos(theta), cos(phi)*cos(theta) ]]) | |
| def T_23(beta): | |
| """ | |
| Transform from Body axes to Zero side slip axes, | |
| Rotation around z-axis by the side-slip angle | |
| """ | |
| return np.array([[cos(beta), -sin(beta), 0], | |
| [sin(beta), cos(beta), 0], | |
| [0, 0, 1]]) | |
| def T_34(alpha): | |
| """ | |
| Transform from Zero side slip axes to Wind axes | |
| Rotation around y-axis by the angle of attack. | |
| """ | |
| return np.array([[cos(alpha), 0, -sin(alpha)], | |
| [0, 1, 0 ], | |
| [sin(alpha), 0, cos(alpha)]]) | |
| def T_14(vec, attitude, beta, alpha): | |
| return matmul(T_34(alpha), matmul(T_23(beta), matmul(T_12(attitude), vec))) | |
| def T_21(attitude): | |
| """ | |
| Transform from Body axes to Earth axes. | |
| Done by transposing the opposite | |
| """ | |
| return np.transpose(T_12(attitude)) | |
| def T_32(beta): | |
| return np.transpose(T_23(beta)) | |
| def T_43(alpha): | |
| return np.transpose(T_34(alpha)) | |
| def T_41(vec, attitude, beta, alpha): | |
| return matmul(T_21(attitude), matmul(T_32(beta), matmul(T_43(alpha), vec))) | |
| def T_31(vec, attitude, beta): | |
| return matmul(T_21(attitude), matmul(T_32(beta), vec)) | |