Open AccessA new approach to the construction of Lagrangians and Hamiltonians for one-dimensional dissipative systems with variable coefficients
Author(s) -
Ding Guang-Tao
Publication year - 2011
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.60.044503
Subject(s) - dissipative system , lagrangian , hamiltonian (control theory) , order (exchange) , physics , first order , variable (mathematics) , differential equation , mathematics , mathematical physics , classical mechanics , mathematical analysis , quantum mechanics , mathematical optimization , finance , economics
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.