(13)
requiring the elliptic integral of the third kind; thence the expression of x1 + x2i and y1 + y2i.
Introducing Euler’s angles θ, φ, ψ,
| x1 = F sin θ sin φ, x2 = F sin θ cos φ, x1 + x2i = iF sin θε−ψi, x3 = F cos θ; |
(14)
| sin θ | dψ | = P sin φ + Q cos φ, |
| dt |
(15)
| F sin2 θ | dψ | = | dT | x1 + | dT | x2 |
| dt | dy1 | dy2 |
| = (qx1 + ry1) x1 + (qx2 + ry2) x2 = q (x12 + x22) + r (x1y1 + x2y2) = gF2 sin2 θ + r (FG − x3y3), |
(16)