The Method of Variation of Parameters for Solving a Dynamical System of Relative Motion

The integration method of a dynamical system of relative motion is studied, and the method of variation of parameters for the dynamical equations of relative motion is presented. First, the dynamic equations of relative motion are brought into the frame of generalized Birkhoffian systems and are expressed in the contravariant algebraic form. Second, an auxiliary system is constructed and its complete solution is found. Finally, the variation of parameters is given, and a complete solution of the problem is obtained by taking advantage of the properties of generalized canonical transformations. An example is given to illustrate the application of the results.