MSC:
37B99,
58F05,
58F35,
70H03,
70H33,
70H35 | MR 1600644 | Zbl 0897.58024 | DOI: 10.21136/MB.1997.126152

Full entry |
PDF
(0.5 MB)
Feedback

Lagrangian system; Lepagean two-form; Euler-Lagrange form; singular Lagrangian; constrained system; Noether theorem; symmetry; constants of motion; first integrals

References:

[1] J. F. Cariñena M. F. Rañada: **Noether's theorem for singular Lagrangians**. Lett. Math. Phys. 15 (1988), 305-311. DOI 10.1007/BF00419588 | MR 0952453

[2] C Ferrario A. Passerini: **Symmetries and constants of motion for constrained Lagrangian systems: a presymplectic version of the Noether theorem**. J. Phys. A 23 (1990), 5061-5081. DOI 10.1088/0305-4470/23/21/040 | MR 1083892

[3] C. Ferrario A. Passerini: **Dynamical symmetries in constrained systems: a Lagrangian analysis**. J. Geom. Phys. 9 (1992), 121-148. DOI 10.1016/0393-0440(92)90016-T | MR 1166718

[4] J. Hrivňák: **Symmetries and first integrals of equations of motion in higher-order mechanics**. Thesis, Dept. of Math., Silesian University, Opava, 1995, pp. 59. (In Czech.)

[5] D. Krupka: **Some geometric aspects of variational problems in fibered manifolds**. Folia Fac. Sci. Nat. UJEP Brunensis 14 (1973), 1-65.

[6] D. Krupka: **A geometric theory of ordinary first order variational problems in fibered manifolds. I. Critical sections, II. Invariance**. J. Math. Anal. Appl. 49 (1975), 180-206; 469-476. DOI 10.1016/0022-247X(75)90169-9 | MR 0362397

[7] D. Krupka: **Geometry of Lagrangean structures 2**. Arch. Math. (Brno) 22 (1986), 211-228. MR 0868536

[8] O. Krupková: **Lepagean 2-forms in higher order Hamiltonian mechanics, I. Regularity, II. Inverse problem**. Arch. Math. (Brno) 22 (1986), 97-120; 23 (1987), 155-170. MR 0868124

[9] O. Krupková: **Variational analysis on fibered manifolds over one-dimensional bases**. PhD Thesis, Dept. of Math., Silesian University, Opava, 1992, pp. 67.

[10] O. Krupková: **Symmetries and first integrals of time-dependent higher-order constrained systems**. J. Geom. Phys. 18 (1996), 38-58. DOI 10.1016/0393-0440(95)00002-X | MR 1370828

[11] G. Marmo G. Mendella W. M. Tulczyjew: **Symmetries and constants of the motion for dynamics in implicit form**. Ann. Inst. Henri Poincaré, Phys. Theor. 57(1992), 147-166. MR 1184887

[12] E. Noether: **Invariante Variationsprobleme**. Nachr. Kgl. Ges. Wiss. Göttingen, Math. Phys. Kl. (1918), 235-257.