pub fn lab_projectile_sc(s: f64, c: f64, mu: f64) -> (f64, f64)Expand description
Lab deflection of the projectile, as (sin psi, cos psi), from the
half-angle sine and cosine of the centre-of-mass angle (s = sin(theta/2),
c = cos(theta/2), s^2 + c^2 = 1) and mu = M1 / M2.
The same relation as in lab_angles, tan(psi) = sin(theta) / (cos(theta) + mu) (Goldstein, Sec. 3.11), written without the angle:
sin theta = 2 s c, cos theta = 1 - 2 s^2, and the vector
(sin theta, cos theta + mu) has length sqrt(1 + 2 mu cos theta + mu^2).
The recoil deflection phi = (pi - theta) / 2 has (sin, cos) = (c, s).