Dynamics of a system of many bodies in space is formulated in a Hamiltonian setting. Typically there are symmetry groups associated to such problems, and one can reduce the phase space by these symmetry groups. Dynamics in the reduced phase space is determined by appropriate Poisson structure. Equilibria for specific cases are obtained and their stability examined using energy-Casimir method. Nonlinear control techniques including exact linearization are applied successfully. A global controllability theorem is proved and feedback stabilization is studied. Applications to robotics and and multibody systems in space are discussed. Symbolic computational tools were used extensively in the research. OOPSS- an Object Oriented Planar System Simulator package has been developed to automatically generate, analyze, simulate and graphically display the dynamics of planar multibody systems.