In this paper,previous research about the dynamic systems in non-inertial system,including methods of establishing dynamics equations are reviewed.

This paper,on the basis of motion kinetics equation,after considering the inertial force,infers the theorem of kinetic energy in non-inertial system.

Principle of d′Alembert Lagrange for a system relative to a non inertial reference frame and non isochronal variation is first presented.

Firstly, this paper presents the D Alembert Lagrange principle of relative to non inertial reference frame in the event space.

This paper studies Lie symmetries and coserved quantities of holonomic systems with unilateral constraints relative to noninertial reference frame.

Routh and Chaplygin equations for variable mass nonlinear nonholonomic system in noninertial reference frame are extended,and the cyclic integral and its condition of existence for the system are given.

In this paper, the D Alembert-Lagrange principle and the generalized chaplygin s equation for variable mass weakly nonholonomio systems moving relative to noninertial reference frame are established at first, and then the generalized energy integral and the generalized cyclic integral of the dynamical equations in the case of one-order approximation for the systems above are studied and presented.

Lagrange equation in noninertial frame and application;

A new type of differential equation for dynamics of noblinear nonholonomic mechanical systems relative to noninertial frame is presented by constructing generalized noninertial potential functions.

In this paper,the generalized equations of variable mass for high-order nonholonomic mechanical system in noninertial frame are de- rived by the universal D Alembert s principle and an example is given to illustrate the application of these equations.

The relative balance in noninertial system can also be coped with by the method of analytical statics.

Having introduced the concept of equal effect-potential energy of intertialthis paper also the discusses tbe condition of mechanical energy conervation in noninertial system.

This article infers the theorem of kinetic energy of the system of particles in noninertial system and analyses the requirement of the conservation of mechanical energy of the system of particles in noninertial system.