相关论文: A note on holonomic costraints
This article deals with the realisation of constraints in underdamped Langevin dynamics via soft-constrained dynamics. Specifically, we study systems with a large (or small) parameter that controls the constraint mechanisms, e.g. the…
Nonholonomic models of automobiles are developed by utilizing tools of analytical mechanics, in particular the Appellian approach that allows one to describe the vehicle dynamics with minimum number of time-dependent state variables. The…
We demonstrate the usefulness of anholonomic frames in the contexts of nonholonomic and vakonomic systems. We take a consistently differential-geometric approach. As an application, we investigate the conditions under which the dynamics of…
The geometric formulation of Hamilton--Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions of the Hamilton--Jacobi problem with the…
In order to increase the efficiency of the computer simulation of biological molecules, it is very common to impose holonomic constraints on the fastest degrees of freedom; normally bond lengths, but also possibly bond angles. However, as…
The principle of least action seems not to lead to equations describing the motion consistent with the physical behaviour, for non-holonomic constraints. Here, a response is proposed for this fundamental problem in Mathematical Physics.…
We consider the question of existence of Hamiltonians for autonomous non-holonomic mechanical systems in this paper. The approach is elementary in the sense that the existence of a Hamiltonian for a given non-holonomic system is considered…
Physical fundamentals of the self-organizing theory for the system with varying constraints are considered. A variation principle, specifically the principle of dynamic harmonization as a generalization of the Gauss-Hertz principle for the…
Variational formulations of statics and dynamics of mechanical systems controlled by external forces are presented as examples of variational principles.
It has been observed that certain classical chains admit topologically protected zero-energy modes that are localized on the boundaries. The static features of such localized modes are captured by linearized equations of motion, but the…
In the Dirac approach to the generalized Hamiltonian formalism, dynamical systems with first- and second-class constraints are investigated. The classification and separation of constraints into the first- and second-class ones are…
Nonholonomic systems are variational models commonly used for mechanical systems with ideal no-slip constraints. This note provides a differential-geometric derivation of the nonholonomic equations of motion for an arbitrary rigid body…
A covariant hamiltonian formalism for the dynamics of compact spinning bodies in curved space-time in the test-particle limit is described. The construction allows a large class of hamiltonians accounting for specific properties and…
In spite of its long history and classical character which goes back even to d'Alembert and Lagrange, the problems of constraints in mechanics of continua is still mysterious and full of misunderstandings. Let us mention the problem of…
This paper investigates a class of Lagrangian control systems with $n$ degrees-of-freedom (DOF) and n-1 actuators, assuming that $n-1$ virtual holonomic constraints have been enforced via feedback, and a basic regularity condition holds.…
We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…
This paper presents a combined strategy for tracking a non-holonomic mobile robot which works under certain operating conditions for system parameters and disturbances. The strategy includes kinematic steering and velocity dynamics learning…
An extension of Riewe's fractional Hamiltonian formulation is presented for fractional constrained systems. The conditions of consistency of the set of constraints with equations of motion are investigated. Three examples of fractional…
One of the founders of the mechanics of nonoholonomic systems is Voronec who published in 1901 a significant generalization of the Caplygin's equations, by removing some restrictive assumptions. In the frame of nonholonomic systems, the…
This paper introduces a novel robust closed-form control law to handle time-varying hard and soft constraints in uncertain high-relative-degree nonlinear MIMO systems. These constraints represent spatiotemporal specifications in mechanical…