Symmetries, first integrals and the inverse problem of Lagrangian mechanics
- 1 September 1981
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 14 (9) , 2227-2238
- https://doi.org/10.1088/0305-4470/14/9/018
Abstract
Deals with the following question: given a symmetry vector field Y of a system of second-order ordinary differential equations, and an associated constant of the motion F, is it possible to find a Lagrangian L for the system, such that Y becomes a Noether symmetry with respect to L, and F its implied Noether constant? For one degree of freedom systems the answer to this question is affirmative. In addition, attention is paid to the construction of a suitable constant of the motion F for given symmetry Y and vice versa. Several examples are discussed.Keywords
This publication has 13 references indexed in Scilit:
- The complete symmetry group of a forced harmonic oscillatorThe Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 1980
- Sl(3,R) and the repulsive oscillatorJournal of Physics A: General Physics, 1980
- The complete symmetry group of the one-dimensional time-dependent harmonic oscillatorJournal of Mathematical Physics, 1980
- Dynamical symmetries and conserved quantitiesJournal of Physics A: General Physics, 1979
- Invariance and conservation laws for Lagrangian systems with one degree of freedomJournal of Mathematical Physics, 1978
- Symmetry groups and conserved quantities for the harmonic oscillatorJournal of Physics A: General Physics, 1978
- Ambiguities in the Lagrangian and Hamiltonian formalism: Transformation propertiesIl Nuovo Cimento B (1971-1996), 1977
- Invariance and Conservation Laws in Classical Mechanics. IIJournal of Mathematical Physics, 1966
- q-Equivalent Particle Hamiltonians. I. The Classical One-Dimensional CaseJournal of Mathematical Physics, 1966
- Invariance and Conservation Laws in Classical MechanicsJournal of Mathematical Physics, 1965