Two results on the completeness of maximal solutions to first and second order ordinary differential equations (or inclusions) over complete Riemannian manifolds, with possibly time-dependent metrics, are obtained. Applications to Lagrangian mechanics and gravitational waves are given.
Completeness of first and second order ODE flows and of Euler–Lagrange equations / Minguzzi, Ettore. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - STAMPA. - 97:(2015), pp. 156-165. [10.1016/j.geomphys.2015.06.010]
Completeness of first and second order ODE flows and of Euler–Lagrange equations
MINGUZZI, ETTORE
2015
Abstract
Two results on the completeness of maximal solutions to first and second order ordinary differential equations (or inclusions) over complete Riemannian manifolds, with possibly time-dependent metrics, are obtained. Applications to Lagrangian mechanics and gravitational waves are given.
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