External Forces:
Listed below are the Forces, acting on the body of air vehicle during flight:
- Drag Force opposite to VT, D
- Lift Forces perpendicular to VT, L
- Side Force, S
So L, D, S defines one coordinate system.
Transformation:
Rotation about y axis by α, and Z axis by β then inverting the components:
D = -Xcosαcosβ – Ysinβ + Zsinαcosβ
D = cosβ(Zsinα – Xcosα) – Ysinβ ………..Eq (1)
S = X cosαsinβ – Ycosα + Zsinαsinβ
S =sinβ ( X cosα + Z sinα) – Ycosβ ……….Eq (2)
L = X sinα – Zcosα ……………………………Eq (3)
Inverting all the equations:
X = Lsinα + (S sinβ – D cosβ )cosα
Y = -(S cosβ + D sinβ)
Z = -Lcosα + (S sinβ – D cosβ)sinα