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

• 来源期刊: 中国物理快报（英文版）
• 年，卷（期）: 2011,（10）
• 页码范围: 146-149
• 页数: 4页
• 语种: 英文
• DOI: 10.1088/0256-307X/28/10/104501

摘要

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.An important direction in analytical dynamics is to present new and versatile integration methods for a complex mechanical system.The motion of a complex system may include the motion of a carrier,as well as the motion of a carried system relative to the carrier.Whittaker[1] studied the Lagrange equations of a holonomic system subject to uniform rotation constraints.Lur'e studied the dynamics of relative motion ofa holonomic system.[2] Mei took the dynamics of relative motion as a special topic to review and research in his monographs.[3-8] Over the past twenty years,research on the dynamics of relative motion has been fruitful.[3- 24]