1,354,654 research outputs found
Some Existence Results for a Singular Elliptic Problem via Bifurcation Theory
Full text linkWe study a semilinear elliptic problem with a singular nonlinear term of the
type , using a variational approach. Note that the minus sign is
important since the corresponding term in the Euler-Lagrange functional is
concave. Contrary to the convex case there are no solutions for the Dirichlet
problem, due to the power being . We therefore study the Neumann problem
and prove a local existence result for solutions bifurcating from constant
solutions. In the radial case we show that one of the two bifurcation branches
is global and unbounded, and we find its asympotic behaviour.Comment: There is a significant problem in the proof of Theorem 2.1: the
"classical bifurcation result for potential operators" quoted at the end of
the proof of 2.1 seems not to be so well known and the cited paper [8] only
covers a very partial case . So a major revision was needed and the author
has came to the conclusion that the revised version should be a new paper,
with a different titl
How to sample a linear mechanical system
No full textVariational integrators is a a new discretization technique of the equations of motion of a mechanical system introduced by Veselov and further developed by J. Marsden an co-workers, which is now widely used by numerical analysts working in various applied fields. This discretization technique, unlike the usual discretization procedures familiar in control, e.g. zero-order-hold, can lead to simple and well-conditioned transformation formulas for the recovery of the continuous time parameters from the discretized model.We discuss variational integrators for linear second order mechanical systems and show that physically meaningful properties of the continuous-time model, like passivity, are preserved. Variational integrator discretization is also shown to provide well-conditioned models for the identification of continuous-time second-orders systems starting from measured data
A pointwise gradient constraint for the Laplace operator. Eigenvalues and bifurca- tion.
No full text
Some elements of subdifferential analysis and some eigenvalue problems for eigenvalue problems.
No full textA virtual rider for motorcycles: Maneuver regulation of a multibody vehicle model
Full text linkThis work develops a virtual rider that can be used to
make a multi-body two-wheeled vehicle follow a specified ground
path with a prescribed velocity profile. The virtual rider system
is based on a simplified motorcycle model, the sliding plane motorcycle,
which is composed of a single rigid body with two ground
contact points. This reduced order nonlinear system was presented
in an earlier work, together with a dynamic inversion procedure
for computing a state-control trajectory corresponding to the desired
task. This dynamic inversion procedure is combined in this
work with a maneuver regulation controller to yield a nonlinear
feedback control strategy. A transverse coordinate system that is
consistent with the mechanical symmetries of ground vehicles is
constructed and used in the development of the maneuver regulation
controller. An inverse optimal control strategy, which also
exploits the mechanical symmetries, is developed to shape the dynamic
response of the closed loop system. Numerical results with
the virtual rider driving amulti-body vehicle through a demanding
maneuver with lateral accelerations reaching 1 g are presented
Multiple Positive Solutions for a Nonsymmetric Elliptic Problem with Concave Convex NonlinearityAnalysis and Topology in Nonlinear Differential Equations
No full textTrajectory exploration of a rigid motorcycle model
No full textThis paper introduces a rigid motorcycle model that
captures many important aspects of real motorcycle dynamics including
sliding and load transfer. The model is used to demonstrate
a dynamic inversion procedure which maps a desired flatland trajectory
into a corresponding (state-input) trajectory for the rigid
motorcycle model. This inverse trajectory is the solution of an optimal
control problem that is computed using the projection operator
approach for the optimization of trajectory functionals, a recently
developed optimization technique. The effectiveness of the
proposed strategy is illustrated using a trajectory computation for
a realistic path that is traversed with a demanding speed profile.
The rigid motorcycle model detailed in this paper is also of interest
as a nontrivial example of a mechanical system with nonideal holonomic
constraints
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