• Research paper •

### A variational principle form for initial value problems in analytical mechanics

Lifu Liang En Luo Xiaojiu Feng

• Received:2006-01-19 Revised:2006-05-12 Online:2007-01-18 Published:2007-01-18

Abstract: According to relations between generalized forces and generalized displacements, convolution are performed between the governing equations of initial value problems in the primary space and the corresponding virtual quantities, and results are added algebraically. A variational principle form for initial value problems in analytical mechanics are then established in the original space, i.e. the variational principles and generalized variational principles in convolution form for initial value problems in analytical mechanics are established in the original space. The stationary conditions of the variational principles and generalized variational principles are deduced. In the meantime, the variational integral method is generalized into the convolutional variational integral method. Using these variational principles and generalized variational principles for initial value problems in analytical mechanics, we can establish models of finite element method and other approximate calculation method and can also find exact solutions of initial value problems in analytical mechanics and transform differential equations into algebraic equations.