Abstract: Kinematics of a flexible multi-body cluster system is described according to a mixed coordinate method. Kinetic energy of the annex and the root body is obtained. Then the quasi-variational principle of flexible multi-body cluster system dynamics with the annex of an extendable translation is established. Applying involutory transformations, the quasi-variational principle of flexible multi-body cluster system dynamics with two kinds of variables is established. Through the deduction of quasi-stationary value conditions of quasi-variational principles, quasi-variational principles have been tested. Finally, according to the quasi-stationary value condition of a Hamiltonian principle on flexible multi-body cluster system dynamics, the vibration differential equation of annex of spacecraft is established.