The Application Of Serret-Andoyer Formalism In External Ballistic

As a branch of classical mechanics,the dynamics of rigid body focuses on the movement of rigid bodies under external forces.As an applied discipline developed on the basis of rigid body dynamics,its development can not be separated from the theoretical study of rigid body dynamics.It can be said that the development of rigid body dynamics theory laid the foundation for the study of external ballistics.In the traditional trajectory,the Eulerian variable is used to establish the six-degree-of-freedom equations.The Serret-Andoyer variable is a special expression for rigid or high-speed rotating rigid bodies movement.Using the canonical transformation,the Euler angle?,?,? and the generalized impulse ?,(48),(37)are transformed into six canonical variables,namely Serret-Andoyer variable?In this paper,the Serret-Andoyer variable is used to establish the motion equations of the projectile under the action of external torque,and the simulation analysis is carried out.Firstly,this paper introduces the basic theory and method of the missile motion equation.This paper introduces the commonly used rigid body attitude description parameters and their advantages and disadvantages.The establishment of the coordinate system and the transformation between the coordinates are the basis for the establishment of the equation of the missiles.After the conversion between the coordinate systems,the equations of rotational motion of the projectile are established.Secondly,the Hamilton mechanics and Lagrange mechanics are introduced briefly.Hamilton mechanics and Lagrange mechanics are different ways of expression in classical mechanics.The classical Euler motion of rigid body around a fixed point problem is given by the Hamilton mechanics and Lagrange mechanics mathematical representation.And further analysis and research on the rigid body rotating freely under the condition of no disturbance.Again,on the basis of the Hamiltonian function,the Serret-Andoyer variable is introduced,and the Euler-Poinsot problem is further analyzed.Finally,using Serret-Andoyer formalism,the projectile motion equations under static moment.Finally,according to the obtained mathematical model,MATLAB / Simulink is used to establish the corresponding simulation model,and the VR module is used to realize the visualization of the state of the missile.The simulation model is used to calculate the results under given initial conditions and to compare and analyze them.The results show that the method can describe the motion of missile.