DSpace Collection:
http://hdl.handle.net/10261/406
Mon, 24 Jan 2022 02:47:59 GMT2022-01-24T02:47:59ZParallel iterative methods for variational integration applied to navigation problems
http://hdl.handle.net/10261/256759
Title: Parallel iterative methods for variational integration applied to navigation problems
Authors: Ferraro, Sebastian J.; Martin de Diego, David; de Almagro, Rodrigo; Sato Martin
Abstract: Discrete variational methods have shown an excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative method for discrete variational methods appropriate for boundary value problems. More concretely, we explore a parallelization strategy that leverages the power of multicore CPUs and GPUs (graphics cards). We study this parallel method for first-order and second-order Lagrangians and we illustrate its excellent behavior in some interesting applications, namely Zermelo's navigation problem, a fuel-optimal navigation problem, and an interpolation problem.Wed, 22 Dec 2021 11:00:02 GMThttp://hdl.handle.net/10261/2567592021-12-22T11:00:02ZThe Herglotz principle and Vakonomic dynamics
http://hdl.handle.net/10261/252982
Title: The Herglotz principle and Vakonomic dynamics
Authors: León Rodríguez, Manuel ; Lainz, Manuel ; Muñoz-Lecanda, Miguel C.
Abstract: In this paper we study vakonomic dynamics on contact systems with nonlinear constraints. In order to obtain the dynamics, we consider a space of admisible paths, which are the ones tangent to a given submanifold. Then, we find the critical points of the Herglotz action on this space of paths. This dynamics can be also obtained through an extended Lagrangian, including Lagrange multiplier terms.
This theory has important applications in optimal control theory for Herglotz control problems, in which the cost function is given implicitly, through an ODE, instead of by a definite integral. Indeed, these control problems can be considered as particular cases of vakonomic contact systems, and we can use the Lagrangian theory of contact systems in order to understand their symmetries and dynamics.Mon, 25 Oct 2021 13:40:02 GMThttp://hdl.handle.net/10261/2529822021-10-25T13:40:02ZThe Geometry of Some Thermodynamic Systems
http://hdl.handle.net/10261/252966
Title: The Geometry of Some Thermodynamic Systems
Authors: Alexandre Anahory Simoes; Martín de Diego, David ; Lainz Valcázar, Manuel ; León Rodríguez, Manuel de
Abstract: In this article, we continue the program started in our previous article of exploring an important class of thermodynamic systems from a geometric point of view. In order to model the time evolution of systems verifying the two laws of thermodynamics, we show that the notion of evolution vector field is adequate to appropriately describe such systems. Our formulation naturally arises from the introduction of a skew-symmetric bracket to which numerical methods based on discrete gradients fit nicely. Moreover, we study the corresponding Lagrangian and Hamiltonian formalism, discussing the fundamental principles from which the equations are derived. An important class of systems that is naturally covered by our formalism are composed thermodynamic systems, which are described by at least two thermal variables and exchange heat between its componentsMon, 25 Oct 2021 12:00:11 GMThttp://hdl.handle.net/10261/2529662021-10-25T12:00:11ZOptimal Trajectory Tracking of Nonholonomic Mechanical Systems: a geometric approach
http://hdl.handle.net/10261/251629
Title: Optimal Trajectory Tracking of Nonholonomic Mechanical Systems: a geometric approach
Authors: Colombo, Leonardo; Martín de Diedo, David; Takuro Sato, Rodrigo
Abstract: We study the tracking of a trajectory for a nonholonomic system by recasting the problem as an optimal control problem. The cost function is chosen to minimize the error in positions and velocities between the trajectory of a non-holonomic system and the desired reference trajectory evolving on the distribution which defines the nonholonomic constraints. We propose a geometric framework since it describes the class of nonlinear systems under study in a coordinate-free framework. Necessary conditions for the existence of extrema are determined by the Pontryagin Minimum Principle. A nonholonomic fully actuated particle is used as a benchmark example to show how the proposed method is applied.Tue, 05 Oct 2021 14:10:03 GMThttp://hdl.handle.net/10261/2516292021-10-05T14:10:03Z