A linear connection associated with any second order differential equation field
There are several problems concerning systems of second-order ordinary differential equations
x= i (t,x j x j )
is the system trivial, i.e. is there a change of coordinates y i = y i (t,x j ) such that the system becomes ÿi = 0?
is the system linear, i.e. is there a change of coordinates which makes the right-hand side linear in yi
is the system separable, i.e. is there a change of coordinates such that the system separates into independent systems of lower dimension?
is the system derivable from a Lagrangian (the inverse problem of the calculus of variations)?
KeywordsVector Field Vector Bundle Linear Connection Horizontal Structure Local Trivialization
Unable to display preview. Download preview PDF.
- 1.M. Crampin, E. Martínez and W. Sarlet. Linear connections for systems of second-order ordinary differential equations. Preprint The Open University, Milton Keynes, UK (1994).Google Scholar
- 4.E. Martínez, J. F. Cariñena. Linear connection induced by an Ehresmann connection on the tangent bundle. Linearization of second-order differential equations. Preprint University of Zaragoza, Spain (1993).Google Scholar
- 5.W. Sarlet, A. Vandecasteele, F.Cantrijn and E.Martínez. Derivations of forms along a map: the framework for time-dependent second-order equations. Diff. Geom. Appl., in press.Google Scholar