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We present a systematic derivation of the constraints that the relativity principle imposes between coefficients of a deformed (but rotational invariant) momentum composition law, dispersion relation, and momentum transformation laws, at…
A methodology for deriving dual variational principles for the classical Newtonian mechanics of mass points in the presence of applied forces, interaction forces, and constraints, all with a general dependence on particle velocities and…
This paper formulates a variational approach for treating observational uncertainty and/or computational model errors as stochastic transport in dynamical systems governed by action principles under nonholonomic constraints. For this…
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…
Variational principles play a central role in classical mechanics, providing compact formulations of dynamics and direct access to conserved quantities. While holonomic systems admit well-known action formulations, non-holonomic systems --…
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.…
A system with anholonomic constraints where the trajectories of physical degrees of freedom are autoparallels on a manifold equipped with a general Cartan connection is discussed. A variational principle for the autoparallel trajectories is…
In this paper, we give sufficient conditions for and deduce a control law under which a mechanical control system converges exponentially fast to a virtual linear nonholonomic constraint that is control invariant via the same feedback…
In a previous article by the author, it was shown that one could effectively give a variational formulation to non-conservative mechanical systems by starting with the first variation functional instead of an action functional. In this…
The paper deals with the problem of integration of equations of motion in nonholonomic systems. By means of well-known theory of the differential equations with an invariant measure the new integrable systems are discovered. Among them…
In this article we study virtual nonholonomic constraints, which are relations between the generalized coordinates and momenta of a mechanical system that can be enforced via feedback control. We design a constraint which emulates…
In this paper we derive the equations of motion for nonholonomic systems subject to inequality constraints, both, in continuous-time and discrete-time. The last is done by discretizing the continuous time-variational principle which defined…
The confusion and ambiguity encountered by students, in understanding virtual displacement and virtual work, is discussed in this article. A definition of virtual displacement is presented that allows one to express them explicitly for…
We consider the fractional generalization of nonholonomic constraints defined by equations with fractional derivatives and provide some examples. The corresponding equations of motion are derived using variational principle.
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 derive a collisionless kinetic theory for an ensemble of molecules undergoing nonholonomic rolling dynamics. We demonstrate that the existence of nonholonomic constraints leads to problems in generalizing the standard methods of…
Vakonomic mechanics has been proposed as a possible description of the dynamics of systems subject to nonholonomic constraints. The aim of the present work is to show that for an important physical system the motion brought about by…
In the framework of the generalized Hamiltonian formalism by Dirac, the local symmetries of dynamical systems with first- and second-class constraints are investigated in the general case without restrictions on the algebra of constraints.…
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…
Virtual constraints are relations imposed in a control system that become invariant via feedback, instead of real physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints on the…