24 citations · 53 across the 3 of their papers we have counts for
4 papers · 1 filter
Semi-basic 1-forms and Helmholtz conditions for the inverse problem of the calculus of variations
Ioan Bucataru, Matias F. Dahl
We use Frölicher-Nijenhuis theory to obtain global Helmholtz conditions, expressed in terms of a semi-basic 1-form, that characterize when a semispray is locally Lagrangian. We als…
Geometric properties of Lagrangian mechanical systems
Ioan Bucataru, Radu Miron
The geometry of a Lagrangian mechanical system is determined by its associated evolution semispray. We uniquely determine this semispray using the symplectic structure and the ener…
Some basic properties of Lagrange spaces
Ioan Bucataru
Consider a regular Lagrangian, the canonical semispray, and the horizontal projector of the canonical nonlinear connection. We prove that if the Lagrangian is constant…
Metric nonlinear connections
Ioan Bucataru
For a system of second order differential equations we determine a nonlinear connection that is compatible with a given generalized Lagrange metric. Using this nonlinear connection…