The Lagrangian and the Generalized Linear Momentum are given in terms of a constant of motion for a one-dimensional autonomous system. The possibility of having an explicit Hamiltonian expression is also analyzed. The approach is applied to some dissipative systems.
Hamiltonian and Lagrangian forN-Dimensional Autonomous Systems
✍ Scribed by G. López
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 244 KB
- Volume
- 251
- Category
- Article
- ISSN
- 0003-4916
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✦ Synopsis
The Lagrangian and the Generalized Linear Momentum are expressed in terms of a Constant of Motion of an N-dimensional autonomous system. The approach allows the construction of Lagrangians and Hamiltonians which are not related by canonical transformations.
📜 SIMILAR VOLUMES
## Abstract We consider the Hamiltonian system in IR^__N__^ given by where __V__ : IR^__N__^ rarr; IR is a smooth potential having a non degenerate local maximum at 0 and we assume that there is an open bounded neighborhood ft of 0 such that V(__x__) < __V__(0) for __x__ δ Ω / {0}, __V(x)__ = __V
We extend the Lagrangian and generalized linear momentum expressions for time-independent systems found by Kobussen and Leubner and by Yan, respectively, to time-dependent systems. Some examples are presented. Chern-Sitnons Theory in the Schriidinger Representation.
An alternative approach to secular problems for Hamiltonian matrices H of regular quasi-one-dimensional systems is suggested. The essence of this approach consists of the inverted order of operations against that of the traditional solid-state theory, viz., taking into account the local structure of