Primary classification of symmetries from the solution manifold in Classical Mechanics

16th Symmetries in Science

Guerrero, J.^1,2 ; Aldaya, V.^2 ; Cossío, F.^2 ; López-Ruiz, F.F.^3

Departamento de Matemática Aplicada, Universidad de Murcia, Campus de Espinardo, Murcia

30100, Spain^1

Instituto de Astrofísica de Andalucía (IAA-CSIC), Apartado Postal 3004, E-Granada

18080, Spain^2

Departamento de Física Aplicada, Universidad de Cádiz, Campus de Puerto Real, Puerto Real, Cádiz

11510, Spain^3

关键词: Classical mechanics;    Classical systems;    Diffeomorphisms;    Non-Hamiltonian;    Point symmetry;    Subalgebras;    Symplectic;    Vector fields;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/538/1/012009/pdf
DOI  :  10.1088/1742-6596/538/1/012009

来源: IOP

【 摘 要 】

The symmetries of the equations of motion of a classical system are characterized in terms of vector field subalgebras of the whole diffeomorphism algebra of the solution manifold (the space of initial constants endowed with a symplectic structure). Among them, naturally arises the subalgebra of Hamiltonian (contact) vector fields corresponding to (jet-prolongued) point symmetries, those not corresponding to point symmetries and the remaining symmetries being associated with non-Hamiltonian (hence non-symplectic) non-strict contact symmetries.