Based on general variation calculus theory, the paper presents the strictly mathematical proof about necessity of norm functional maximum-minimum value existence in condition of integral item restriction, develops optimal mathematical model on the question of the speediest fall in condition of non-obstructing free fall and obstructing free fall, and shows how to solve them.

Deals with the form invariance and the conserved quantities of a Lagrange system forced by holonomic constraints.

The motion of the rolling disk was analysed to try to explain some unintegrable equations of constraint which is not definitely independent equation of nonholonomic constraint,and the concept of concealed coordinate was proposed.

Some rules for dealing with the integrity constraints are presented by analyzing the different types of integrity constraints in schema integration multidatabase systems.

This paper proposes a kind of method that can preserve integrity constraints in data mapping,contrives a mechanism(DAPPIC)of generating constraints-preserving publishing rules.

For this purpose,this paper analyses briefly the semantic constraints characteristics in both XML schema and relation schema,and gives the detailed introduction about the conversion methods from the semantic constraints of XML schema to the integrity constraints of relation schema.

The design of underactuated manipulator based on nonholonomic constraint theory;

Effects of non-conservative forces and nonholonomic constraints on Noether symmetries of a Lagrange system;

Effects of non-conservative forces and nonholonomic constraints on Lie symmetries of a Hamiltonian system;