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Title: | Cubic invariants of one-dimensional Lagrangian systems | Authors: | Simić, Srboljub | Issue Date: | 1-Dec-2000 | Journal: | International Journal of Non-Linear Mechanics | Abstract: | In this paper we consider conservation laws of the third degree with respect to ẋ of the one-dimensional time-dependent Lagrangian systems ẍ = - ∂Π/∂x. The analysis is based on the Noetherian approach. It is shown that the existence of conservation laws, as well as their structure depend on the solution of a system of first-order partial differential equations - so-called generalized Killing's equations. It is demonstrated that due to specific structure of the generators of infinitesimal transformations a rather general algorithm for derivation of cubic invariants could be established. Several types of potential Π(t,x) which admit the existence of cubic invariants are determined. | URI: | https://open.uns.ac.rs/handle/123456789/14437 | ISSN: | 00207462 | DOI: | https://doi.org/10.1016/S0020-7462(99)00021-9 |
Appears in Collections: | PMF Publikacije/Publications |
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