A variational principle form for initial value problems in analytical mechanics

According to relationsbetween generalized forces and generalized displacements,convolution are performed between the governingequations of initial value problems in the primary space and the corresponding virtual quantities, and results are added algebraically.A variational principle form for initial valueproblems in analytical mechanics are then established in the original space, i.e.the variational principles and generalized variational principlesin convolution form for initialvalue problems in analytical mechanics are established in the originalspace. The stationary conditions of the variational principles andgeneralized variational principles are deduced. In the meantime, the variational integral method is generalized intothe convolutional variational integral method. Using these variationalprinciples and generalized variational principles for initial value problemsin analytical mechanics, we can establish models of finite elementmethod and other approximate calculation method and can also find exactsolutions of initial valueproblems in analytical mechanics and transform differentialequations into algebraic equations.