This paper infers the dynamical equation of relative motion by introducing the concept of generalized potential;and illustrates its application with examples.

The generalized potential concept was introduced,the Lagrange function and the Lagrange equation which are of the ideally,entirely constrained irrotational mechanics system related to non intertial system was infered by using the Hamilton theory.

The theorem of existence of the generalized potential has been established.

Based on generalized inertial potential,this paper first gives new type of motion e-quation for nonholonomic relative motion dynamical systems,and then discusses constructing methodof in tegral in variance for these systems,finally obtains Noether s theorem and its inverse theorem.

However, Largrange’s equation of the second kind of the ideal and holonomic constraint force systems is gave in this paper, beginning from generalized inertial potential to the non-inertial reference system, and Foucault’s pendulum regular of motion is solved by this analysis mechanics method.

The results show that the general chemical potential not only expands the chemical potential definition of the classical thermodynamics and field of application,but also indicates the connotation of external physical fields contribution to the chemical potential and effect on the.

A generalized potential function U has to be found from the formula of inertia force in noninertia system and the analogous Lagrangefunction L”,then we get the second type Lagrange equation in noninertia system and the Lagrange equation in a potential field,which is anothermethod of answermg dynamic problems in noninertia system of analytic mechanics.

This paper has qualitatively discussed the Coriol is field of force and introduced the generalized inertia potential.