相关论文: On Virtual Displacement and Virtual Work in Lagran…
The confusion and ambiguity encountered by students, in understanding virtual displacement and virtual work, is addressed in this article. A definition of virtual displacement is presented that allows one to express them explicitly for both…
Lagrangian mechanics uses d'Alembert's principle of zero virtual work as an important starting point. The orthogonality of the force of constraint and virtual displacement is emphasized in literature, without a clear warning that this is…
In the context of holonomic constrained systems the identification of virtual displacements is clear and consolidated: this gives the possibility, once the class of displacements have been combined with Newton's equations, to write the…
The aim of this paper is to show that the Lagrange-d'Alembert and its equivalent the Gauss and Appel principle are not the only way to deduce the equations of motion of the nonholonomic systems. Instead of them, here we consider the…
We present the principle of virtual action as a foundation of continuum mechanics. Used mainly in relativity, the method has a useful application in classical mechanics and places the notion of action as the basic concept of dynamics. The…
This paper investigates the dynamics of nonholonomic mechanical systems, focusing on fundamental variational assumptions and the role of the transpositional rule. We analyze how the Cetaev condition and the first variation of constraints…
This paper investigates the dynamics of nonholonomic mechanical systems, with a particular focus on the fundamental variational assumptions and the role of the transpositional rule. We analyze how the $\check Cetaev condition and the first…
This paper presents a coordinate-free formulation of virtual holonomic constraints for underactuated Lagrangian control systems on Riemannian manifolds. It is shown that when a virtual constraint enjoys a regularity property, the…
We propose an extension of the principle of virtual work of mechanics to random dynamics of mechanical systems. The total virtual work of the interacting forces and inertial forces on every particle of the system is calculated by…
We construct an operational formulation of classical mechanics without presupposing previous results from analytical mechanics. In doing so, several concepts from analytical mechanics will be rediscovered from an entirely new perspective.…
We propose a new description of dynamics of autonomous mechanical systems which includes the momentum-velocity relation. This description is formulated as a variational principle of virtual action more complete than the Hamilton Principle.…
The constraint distribution in non-holonomic mechanics has a double role. On one hand, it is a kinematic constraint, that is, it is a restriction on the motion itself. On the other hand, it is also a restriction on the allowed variations…
In this paper, we present a Lagrangian formalism for nonequilibrium thermodynamics. This formalism is an extension of the Hamilton principle in classical mechanics that allows the inclusion of irreversible phenomena in both discrete and…
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.…
Virtual constraints are invariant relations imposed on a control system via feedback as opposed to real physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints on the…
We discuss a recently proposed variational principle for deriving the variational equations associated to any Lagrangian system. The principle gives simultaneously the Lagrange and the variational equations of the system. We define a new…
We propose a new classical approach for describing a system composed of $n$ interacting particles with variable mass connected by a single field with no predefined form ($n$-VMVF systems). Instead of assuming any particular nature or…
Motions of continuous media presenting singularities are associated with phenomena involving shocks, interfaces or material surfaces. The equations representing evolutions of these media are irregular through geometrical manifolds. A unique…
Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is…
In this note we present invariant formulation of the d'Alambert principle and classical time-dependent Lagrangian mechanics with holonomic constraints from the perspective of moving frames.