| 积分二阶线性非完整力学系统的最终乘子方法 |
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| 引用本文： | 张毅. 积分二阶线性非完整力学系统的最终乘子方法[J]. 苏州科技学院学报(自然科学版), 2012, 29(1): 7-12 |
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| 作者姓名： | 张毅 |
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| 作者单位： | 苏州科技学院土木工程学院,江苏苏州,215011 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 研究二阶线性非完整力学系统的积分方法。建立了相空间中二阶线性非完整力学系统的运动微分方程，给出了系统的Jacobi最终乘子的定义，研究了系统的第一积分与Jacobi最终乘子的关系。研究表明：由n个广义坐标确定的受有g个二阶非完整约束的力学系统，如果已知系统（2n-1）个第一积分，则可利用Jacobi最终乘子给出系统的解。文末举例说明结果的应用。
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| 关 键 词： | 二阶非完整系统 运动微分方程 积分方法 Jacobi最终乘子 |
An integration method of a mechanical system with second order linear non-holonomic constraints |
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| ZHANG Yi. An integration method of a mechanical system with second order linear non-holonomic constraints[J]. Journal of University of Science and Technology of Suzhou, 2012, 29(1): 7-12 |
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| Authors: | ZHANG Yi |
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| Affiliation: | ZHANG Yi(College of Civil Engineering,SUST,Suzhou 215011,China) |
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| Abstract: | A new integration method of a mechanical system with second order linear non-holonomic constraints is put forward.The differential equations of motion of the mechanical system with second order linear non-holonomic constraints in phase space are established.The Jacobi Last Multiplier of the system is defined and the relation between the Jacobi Last Multiplier and the first integrals of the system is discussed.The study shows that for a mechanical system with g second order linear non-holonomic constraints,whose configuration is determined by n generalized coordinates,the solution of the system can be found by the Jacobi Last Multiplier if(2n-1) first integrals of the system are known.An example is given to illustrate the application of the results. |
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| Keywords: | second order non-holonomic system differential equations of motion integration method Jacobi LastMultiplier |
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