Forced Angles and Polynomal expresion Formulas.
I run this small Formula based expression on Auto Cad 3d 2004. Using a constant of 2.2 as vector 1. Drag is interpilated by random subtraction and becomes a non variant at the outcome. Angle is not constant as tragectory is determined by Vector 1 x velocity sq.
sinh(x) = ( e^{x} - e^{-x} )/2
csch(x) = 1/sinh(x) = 2/( e^{x} - e^{-x} )
cosh(x) = ( e x + e -x )/2
sech(x) = 1/cosh(x) = 2/( e^{x} + e^{-x} )
tanh(x) = sinh(x)/cosh(x) = ( e^{x} - e^{-x} )/( e^{x} + e^{-x} )
coth(x) = 1/tanh(x) = ( e^{x} + e^{-x})/( e^{x} - e^{-x} )
|<a, b>| = magnitude of vector = (a 2+ b 2)
|<x1, .., xn>| = (x12+ .. + xn2)
<a, b> + <c, d> = <a+c, b+d>
<x1, .., xn> + <y1, .., yn>= < x1+y1, .., xn+yn>
k <a, b> = <ka, kb>
k <x1, .., xn> = <k x1, .., k x2>
(a+b) 2 = a 2 + 2ab + b 2
(a+b)(c+d) = ac + ad + bc + bd
a 2 - b 2 = (a+b)(a-b) (Difference of squares)
a 3 b 3 = (a b)(a 2 ab + b 2) (Sum and Difference of Cubes)
x 2 + (a+b)x + AB = (x + a)(x + b)
if ax 2 + bx + c = 0 then x = ( -b (b 2 - 4ac) ) / 2a (Quadratic Formula)