RT Journal Article
T1 Parameter-invariant second-order variational problems in one variable
A1 Muñoz Masqué, Jaime
A1 Pozo Coronado, Luis Miguel
AB A projection is defined such that a second-order Lagrangian density factors through this projection module contact forms if and only if it is parameter invariant. In this way, a geometric interpretation of the parameter invariance conditions is obtained. The above projection is then used to prove the strict factorization of the Poincare-Cartan form attached to a parameter-invariant variational problem thus leading us to state the Hamilton-Cartan formalism, the complete description of symmetries and regularity for such problems. The case of the squared curvature Lagrangian in the plane is analysed especially.
PB Iop science
SN 0305-4470
YR 1998
FD 1998
LK https://hdl.handle.net/20.500.14352/57772
UL https://hdl.handle.net/20.500.14352/57772
LA eng
NO Abate M and Patrizio G 1994 Finsler Metrics—A Global Approach (Lecture Notes in Mathematics 1591)(New York: Springer)Atiyah M F and MacDonald I G 1969 Introduction to Commutative Algebra (Reading, MA: Addison-Wesley)[3] Bao D and Chern S S 1993 On a notable connection in Finsler geometry Houston J. Math. 19 135–80Batlle C, Gomis J, Pons J M and Rom´an-Roy N 1988 Lagrangian and Hamiltonian constraints for secondordersingular Lagrangians J. Phys. A: Math. Gen. 21 2693–703Blaschke W 1930 Vorlesungenuber Differentialgeometrie vol I 3rd edn (Berlin: Springer)Bryant R and Griffiths P 1986 Reduction for constrained variational problems and R k2ds Am. J. Math. 108 525–70Constantelos G C 1984 On the Hamilton–Jacobi theory with derivatives of higher order Riv. Nuovo Cimento B 84 91–101Giaquinta M and Hildebrandt S 1996 Calculus of Variations II: The Hamiltonian Formalism (Berlin: Springer)Godbillon C 1969 Geometrie Differentielle et Mecanique Analytique (Paris: Hermann)Goldschmidt H 1967 Integrability criteria for systems of non-linear partial differential equations J. Diff.Geom. 1 269–307Goldschmidt H and Sternberg S 1973 The Hamilton–Cartan formalism in the calculus of variations Ann. Inst.Fourier 23 203–67Grifone J 1972 Structure presque-tangente et connections II Ann. Inst. Fourier Grenoble 22 291–338Guggenheimer H W 1963 Differential Geometry (New York:McGraw-Hill)
NO CICYT
DS Docta Complutense
RD 28 abr 2024