File:Space-time diagram for family of true trajectories.png

Vectorized version of image.

Space-time diagram for a family of true trajectories x(t) for the quartic oscillator [V(x) = (1/4)Cx^4] starting at P(0,0) with v_0 > 0. For this particular oscillator the kinetic focus occurs at a fraction 0.646 of the half-period T_0/2, illustrated here for trajectory 0. The kinetic foci of all true trajectories of this family lie along the heavy gray line, the caustic. Squares indicate recrossing events of true trajectory 0 with the other two true trajectories. (From Gray and Taylor 2007.)