Variational contact symmetries of constrained Lagrangians

JOURNAL OF GEOMETRY AND PHYSICS

卷:101

Article

Terzis, Petros A.¹  Dimakis, N.²  Christodoulakis, T.¹  Paliathanasis, Andronikos²  Tsamparlis, Michael³ 

[1] Univ Athens, Dept Phys, Nucl & Particle Phys Sect, GR-15771 Athens, Greece

[2] Univ Austral Chile, Inst Ciencias Fis & Matemat, Valdivia, Chile

[3] Univ Athens, Dept Phys, Sect Astron Astrophys & Mech, Athens 15783, Greece

关键词: Constrained systems;    Noether symmetries;    Integrable systems;    Symmetries of differential equations;   

DOI  :  10.1016/j.geomphys.2015.12.003

来源: Elsevier

【 摘 要 】

The investigation of contact symmetries of re-parametrization invariant Lagrangians of finite degrees of freedom and quadratic in the velocities is presented. The main concern of the paper is those symmetry generators which depend linearly in the velocities. A natural extension of the symmetry generator. along the lapse function N(t), with the appropriate extension of the dependence in N(t) of the gauge function, is assumed; this action yields new results. The central finding is that the integrals of motion are either linear or quadratic in velocities and are generated, respectively by the conformal Killing vector fields and the conformal Killing tensors of the configuration space metric deduced from the kinetic part of the Lagrangian (with appropriate conformal factors). The freedom of re-parametrization allows one to appropriately scale N(t), so that the potential becomes constant; in this case the integrals of motion can be constructed from the Killing fields and Killing tensors of the scaled metric. A rather interesting result is the non-necessity of the gauge function in Noether's theorem due to the presence of the Hamiltonian constraint. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free