Fractional Damping Through Restricted Calculus of Variations

We deliver a novel approach towards the variational description of Lagrangian mechanical systems subject to fractional damping by establishing restricted Hamilton’s principle. Fractional is particular instance non-local (in time) damping, which ubiquitous in engineering applications. The principle relies on including derivatives state space, doubling curves (which implies an extra mirror system) and restriction class varied curves. will obtain correct dynamics show rigorously that nothing but principal one reversed time; thus, not adding physics original system. price pay, other hand, damped only sufficient condition for extremals action. In addition, we proceed discretise new This discretisation provides set numerical integrators continuous denote Variational Integrators (FVIs). discrete obtained upon same ingredients, say variations. display performance FVIs, have local truncation order 1, two examples. As with origin, those generated Lagrange–d’Alembert principle, they superior tracking dissipative energy, opposition direct (order 1) discretisations equations, such as explicit implicit Euler schemes.