ABSTRACT
Thus, PK’s trajectory satisfies the [second-order linear ordinary differential] equation of motion
d2x
dt2 = −ω2 x .
(5) Solutions to this equation of motion may be obtained by a variety of means.
method one: [ Rote Recognition ]
Two elementary mathematical facts,
d cos(x)
dx = − sin(x) and d sin(x)
dx = cos(x) ,
iterated [in either order] reveal that both sine and cosine can be employed to construct putative dynamical trajectories:
x(t) = A cos(ω t) +B sin(ω t) .
