  We study the stability of particles in slip-stacking configuration, used to
nearly double proton beam intensity at Fermilab. We introduce universal area
factors to calculate the available phase space area for any set of beam
parameters without individual simulation. We find perturbative solutions for
stable particle trajectories. We establish Booster beam quality requirements to
achieve 97\% slip-stacking efficiency. We show that slip-stacking dynamics
directly correspond to the driven pendulum and to the system of two
standing-wave traps moving with respect to each other.
