Abstract: The momentum conditions at the time tp are explained as the impulse body forces by means of Delta function △(t-tp). Based on this point, the definitions of the action of momentum potential at the time terminal tp -gp (ui) and its complementary one-gp(pi)are formulated, respectively. The two parameters q and q' ,q + q* = 1, are introduced. Furthermore, some variational principles for nonlinear elastodynamics are developed. They are the variational principles of potential energy action, the one of complementary energy action, the two forms of generalized potential energy action and the two forms of generalized complementary energy action. It may be attractive that initial value conditions or the final value ones are remained in the stationary conditions of these variational principles.

Key words: variational principles, initial value problems, final value problems, nonlinear mechanics, elastodynamics