摘要
提出构造二阶微分方程的Lagrange函数和Hamilton函数的新路径.将二阶方程写成一阶方程组并构造出对应的一阶Lagrange函数后,直接从一阶Lagrange函数导出二阶Lagrange函数和Hamilton函数.利用上述方法得到若干耗散和类耗散系统的一阶和二阶Lagrange函数以及Hamilton函数;讨论了这种方法的优点.举例说明所得结果的应用.
A new approach to the construction of Lagrangian and Hamiltonian for a second-order differential equation is presented.By writing the second-order equation in the first-order form and constructing first-order Lagranian corresponding to the set of the first-order equations,the second-order Lagrangian and Hamiltionian are deduced from the first-order Lagrangian directly.By using the above method the first-order ane the second-order Lagrangians and the Hamiltonians for some of dissipative and dissipative-like systems are obtained.The advantage of the approach is discussed.Four examples are given to illustrate the applications of the results.
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2011年第4期327-331,共5页
Acta Physica Sinica
