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acceleration aerodynamic forces aerodynamic stability derivatives aeronautical aircraft angular velocity angular velocity components assume the following axis base vectors bivector body axes Christoffel symbols coefficients coordinate transformation equations COS(A COS(A)COS(B)SIN(B COS(A)SIN(A)COS(B COS(A)SIN(A)SIN(B COS(A)SIN(B COS(B cos2 covariant and contravariant covariant derivative curvilinear coordinate curvilinear coordinate system denoted derivatives with respect differential dt dt Earth-fixed equa equations of motion Euler angle following form forces and moments formulation gravitational Hence indices inertia J:1 THRU MACSYMA mathematical MATRIX-ENTERED metric tensors mixed tensor models msec Navier-Stokes equations notation obtained orthogonal Cartesian output particle physical components polar coordinate system rate of change Ricci tensor ROW 3 COLUMN scalar second kind SIN(A SIN(A)COS(B)SIN(B SIN(A)SIN(B SIN(B sin2 x2 static forces substitution from equation summation convention tensor components tensor of rank thrust vector tion transformation law velocity vector wind axes wind-tunnel axes