  The purpose of this paper is to consider flocking formations of a second
order dynamic system on a sphere with a Cucker-Smale type flocking operator and
cooperative control. The flocking operator consists of a weighted control
parameter and a natural relative velocity. The cooperative control law is given
by a combination of attractive and repulsive forces. We prove that the solution
to this system converges to an asymptotic spherical configuration depending on
the control parameters of the cooperative control law. All possible asymptotic
configurations for this system are classified and sufficient conditions for
rendezvous, deployment, and local deployment, respectively, are presented. In
addition, we provide several numerical simulations to confirm our analytic
results. We numerically verify that the solution to this system converges to a
formation flight with a nonzero constant speed if we add a boost term. The
flocking operator acts as a stabilizer on the spherical cooperative control
laws.
