A new approach to the construction of Lagrangians and Hamiltonians for one-dimensional dissipative systems with variable coefficients | Zendy

Ding Guang-Tao | Zendy

Open Access

A 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 -

acta physica sinica

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.

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