Generalized Variational Principles in General Mechanics and Their Applications

摘要

In mechanics of deformable body, generalized variational principles have been widely used in the finite element method and other approximate computing methods. This kind of application can be spread into general mechanics. That is one of the significance to study generalized variational principles in general mechanics. On the basis of the references [2], [3], [4], [5] and [6], this paper establishes generalized variational principles of two and three kinds of variables of holonomic and non -holonomic systems. Their popularization and application are discussed. The general notation: x -rectangular coordinates, q_s -general coordinates, t-time, x_k - derivatives of x_k, q_s - derivatives of q_s, v_k -velocity, v_s~q - general velocity, P_k -momentum, P_s~q - general momentum, P_k -derivatives of P_k , p_s~q - derivatives of P_s~q, T-kinetic energy, V-potential energy.