Jacobi equations using a variational principle
Núñez-Yépez, H. N. ; Salas-Brito, A. L.
arXiv, 0005005 / Harvested from arXiv
Text on arXiv
A variational principle is proposed for obtaining the Jacobi equations in systems admitting a Lagrangian description. The variational principle gives simultaneously the Lagrange equations of motion and the Jacobi variational equations for the system. The approach can be of help in finding constants of motion in the Jacobi equations as well as in analysing the stability of the systems and can be related to the vertical extension of the Lagrangian formalism. To exemplify two of such aspects, we uncover a constant of motion in the Jacobi equations of autonomous systems and we recover the well-known sufficient conditions of stability of two dimensional orbits in classical mechanics.
Publié le : 2000-05-02
Classification:  Mathematical Physics,  Mathematics - Differential Geometry,  Mathematics - Dynamical Systems,  Nonlinear Sciences - Exactly Solvable and Integrable Systems,  Physics - Classical Physics 
@article{0005005,
     author = {N\'u\~nez-Y\'epez, H. N. and Salas-Brito, A. L.},
     title = {Jacobi equations using a variational principle},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0005005}
}

Núñez-Yépez, H. N.; Salas-Brito, A. L. Jacobi equations using a variational principle. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0005005/