Complete separability of time-dependent second-order ordinary differential equations

Acta Applicandae Mathematicae

Volumn 42, Issue 3, 1996, Pages 309-334

  Cantrijn, F ^a,c   Sarlet, W ^a   Vandecasteele, A ^a   Martinez E ^b  

^a GHENT UNIVERSITY   (Belgium)

^b UNIVERSITY OF ZARAGOZA   (Spain)

^c FUND FOR SCIENTIFIC RESEARCH   (Belgium)

Author keywords

Derivations; Forms along a map; Separability; Time dependent second order equations

Indexed keywords

EID: 0038909120     PISSN: 01678019     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01064171     Document Type: Article

References (14)

1. Benenti, S.: Separation of Variables in the Geodesic Hamilton-Jacobi Equation, in P. Donato et al. (eds), Symplectic Geometry and Mathematical Physics, Progress in Math. 99, Birkhäuser, Basel, 1991, pp. 1-35.
2. Crampin, M., Prince, G. E., and Thompson, G.: A geometrical version of the Helmholtz conditions in time-dependent Lagrangian dynamics, J. Phys. A: Math. Gen. 17 (1984), 1437-1447.
3. de León, M. and Rodrigues, P. R.: Methods of Differential Geometry in Analytical Mechanics, Mathematics Studies 158, North-Holland, Amsterdam, 1989.
4. de León, M. and Martín de Diego, D.: Nonautonomous submersive second-order differential equations and Lie symmetries, Internat. J. Theoret. Phys. 33 (1994), 1759-1781.
5. Ferrario, C., Lo Vecchio, G., Marmo, G., and Morandi, G.: A separability theorem for dynamical systems admitting alternative Lagrangians, J. Phys. A: Math. Gen. 20 (1987), 3225-3236.
6. Frölicher, A. and Nijenhuis, A.: Theory of vector valued differential forms, Proc. Ned. Acad. Wetensch. Sér. A 59 (1956), 338-359.
7. Kalnins, E. G.: Separation of Variables for Riemannian Spaces of Constant Curvature, Pitman Monographs in Pure and Appl. Math. 28, Longman Sci. & Technical, Essex, 1986.
8. Kossowski, M. and Thompson, G.: Submersive second-order differential equations, Math. Proc. Camb. Phil. Soc. 110 (1991), 207-224.
9. Martínez, E., Cariñena, J. F., and Sarlet, W.: Geometric characterization of separable second-order differential equations, Math. Proc. Camb. Phil. Soc. 113 (1993), 205-224.
10. Martínez E., Cariñena, J. F. and Sarlet, W.: Derivations of differential forms along the tangent bundle projection, Differential Geom. Appl. 2 (1992), 17-43.
11. Martínez, E., Cariñena, J. F., and Sarlet, W.: Derivations of differential forms along the tangent bundle projection II, Differential Geom. Appl. 3 (1993), 1-29.
12. Sarlet, W., Cantrijn, F., and Martínez, E.: Application of the theory of separability of second-order differential equations, J. Nonlinear Math. Phys. 1 (1994), 5-24.
13. Sarlet, W., Vandecasteele, A., Cantrijn, F., and Martínez, E.: Derivations of forms along a map: the framework for time-dependent second-order equations, Differential Geom. Appl. 5 (1995), 171-203.
14. Saunders, D. J.: The Geometry of Jet Bundles, London Math. Soc. Lect. Notes Series 142, Cambridge University Press, 1989.