Classical Mechanics with Inequality Constraints and Gravity Models with Limiting Curvature

Abstract

In this paper, we discuss mechanical systems with inequality constraints Φ(q,q˙,...)≤0. We demonstrate how such constraints can be taken into account by proper modification of the action which describes the original unconstrained dynamics. To illustrate this approach, we consider a harmonic oscillator in the model with limiting velocity. We compare the behavior of such an oscillator with the behavior of a relativistic oscillator and demonstrate that when the amplitude of the oscillator is large, the properties of both types of oscillators are quite similar. We also discuss inequality constraints, which contain higher derivatives. At the end of the paper, we briefly discuss possible applications of the developed approach to gravity models with limiting curvature.

Keywords

• classical mechanics
• Lagrangian formulation
• limiting curvature
• gravity models