Completeness of the Trajectories of Particles Coupled to a General Force Field

Abstract

We analyze the extendability of the solutions to a certain second order differential equation on a Riemannian manifold $(M,g)$, which is defined by a general class of forces (both prescribed on $M$ or depending on the velocity). The results include the general time-dependent anholonomic case, and further refinements for autonomous systems or forces derived from a potential are obtained. These extend classical results for Lagrangian and Hamiltonian systems. Several examples show the optimality of the assumptions as well as the applicability of the results, including an application to relativistic pp-waves.

Archive for Rational Mechanics and Analysis (to appear)

References in corpus (1)

• The causal boundary of wave-type spacetimes

Cited by in corpus (9)

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• Embedding nonrelativistic physics inside a gravitational wave
• Completeness of general pp-wave spacetimes and their impulsive limit
• Ehlers-Kundt Conjecture about Gravitational Waves and Dynamical Systems
• Completeness of trajectories of relativistic particles under stationary magnetic fields
• Remarks on the completeness of trajectories of accelerated particles in Riemannian manifolds and plane waves
• Completeness of first and second order ODE flows and of Euler-Lagrange equations
• The globally hyperbolic metric splitting for non-smooth wave-type space-times
• Completeness of Riemannian metrics: an application to the control of constrained mechanical systems