Feedback Integrators for Nonholonomic Mechanical Systems
نویسندگان
چکیده
منابع مشابه
Integrators for Nonholonomic Mechanical Systems
We study a discrete analog of the Lagrange-d’Alembert principle of nonhonolomic mechanics and give conditions for it to define a map and to be reversible. In specific cases it can generate linearly implicit, semi-implicit, or implicit numerical integrators for nonholonomic systems which, in several examples, exhibit superior preservation of the dynamics. We also study discrete nonholonomic syst...
متن کاملVariational Integrators for Hamiltonizable Nonholonomic Systems
We report on new applications of the Poincaré and Sundman timetransformations to the simulation of nonholonomic systems. These transformations are here applied to nonholonomic mechanical systems known to be Hamiltonizable (briefly, nonholonomic systems whose constrained mechanics are Hamiltonian after a suitable time reparameterization). We show how such an application permits the usage of vari...
متن کاملNonholonomic Integrators
We introduce a discretization of the Lagrange-d’Alembert principle for Lagrangian systems with nonholonomic constraints, which allows us to construct numerical integrators that approximate the continuous flow. We study the geometric invariance properties of the discrete flow which provide an explanation for the good performance of the proposed method. This is tested on two examples: a nonholono...
متن کاملOn the Construction of Variational Integrators for Optimal Control of Nonholonomic Mechanical Systems
In this paper we derive variational integrators for optimal control problems of nonholonomic mechanical systems. We rewrite the system as a constrained second-order variational problem, that is, as a problem where the Lagrangian and constraints are defined in terms of the position, velocity and the acceleration of the system. Instead of discretizing directly the equations of motion, we discreti...
متن کاملEnergy Conserving Nonholonomic Integrators
We address the problem of constructing numerical integrators for nonholonomic Lagrangian systems that enjoy appropriate discrete versions of the geometric properties of the continuous flow, including the preservation of energy. Building on previous work on time-dependent discrete mechanics, our approach is based on a discrete version of the Lagrange-d’Alembert principle for nonautonomous systems.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Nonlinear Science
سال: 2018
ISSN: 0938-8974,1432-1467
DOI: 10.1007/s00332-018-9514-6