Related papers: Constrained Systems and Analytical Mechanics in Sp…

A comparison between the two possible variational principles for the study of a free falling spinless particle in a space-time with torsion is noted. It is well known that the autoparallel trajectories can be obtained from a variational…

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…

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…

Recently it has been argued that autoparallels should be the correct description of free particle motion in spaces with torsion, and that such trajectories can be derived from variational principles if these are suitably adapted. 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…

We give a geometric description of variational principles in mechanics, with special attention to constrained systems. For the general case of nonholonomic constraints, a unified variational approach is given, and the equations of motion of…

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.…

We present a simpler and more powerful version of the recently-discovered action principle for the motion of a spinless point particle in spacetimes with curvature and torsion. The surprising feature of the new principle is that an action…

The Hamiltonian description for a wide class of mechanical systems, having local symmetry transformations depending on time derivatives of the gauge parameters of arbitrary order, is constructed. The Poisson brackets of the Hamiltonian and…

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…

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…

We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid…

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.…

I consider the equations of motion which follow from d'Alembert's principle for a general mechanical system in a space of N dimensions, constrained by a non-holonomic constraint which is linear and homogeneous in the generalised velocities.…

As a contribution to the ongoing discussion of trajectories of spinless particles in spaces with torsion we show that the geometry of such spaces can be induced by embedding their curves in a euclidean space without torsion. Technically…

This paper studies nonsmooth variational problems on principal bundles for nonholonomic systems with collisions taking place in the boundary of the manifold configuration space of the nonholonopmic system. In particular, we first extended…

We prove that autoparallel curves associated with a torsion-free but not necessarily metric-compatible affine connection can be derived from an action principle. We explicitly construct the action functional and show by standard variational…

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 consider a geometric framework for analytical mechanics with external forces. Four versions of this framework are considered. A variational principle with boundary terms and external forces.The second and the third versions are the…

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…