A Discussion of the Quasi-Euler–Lagrange Equation

Autor:	William Roger Fuller
Rok vydání:	1992
Předmět:	Euler–Lagrange equation Constant coefficients Partial differential equation Dynamical systems theory Applied Mathematics Mathematical analysis Dynamical system Vector-valued function Harmonic oscillator Mathematics Analytic function
Zdroj:	SIAM Journal on Applied Mathematics. 52:870-882
ISSN:	1095-712X 0036-1399
DOI:	10.1137/0152049
Popis:	The quasi-Euler–Lagrange equation, $a(x) \cdot \operatorname{grad} (\partial _1 L) + b(x) \cdot \operatorname{grad} (L) = 0$, is introduced and is shown to be locally solvable when $a(x)$ and $b(x)$ are analytic vector functions. A general solution is constructed when the equation is linearized with respect to $x_1 $. Examples are considered in the constant coefficient case, and applications are made to the construction of time-independent Lagrangians and also to the construction of quasi-Lagrangians for dynamical systems.
Databáze:	OpenAIRE
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