相关论文: Nonholonomic constrains: why does not the least ac…

In this paper we use an affine connection formulation to study an optimal control problem for a class of nonholonomic, under-actuated mechanical systems. In particular, we aim at minimizing the norm-squared of the control input to move the…

The least action principle is established for the dynamics of a test particle in a dilaton-Maxwell background. These dynamics and background are invariant under the action of the dilatation transformation; explicit form of the corresponding…

When generalizing the principle of least action for fields containing higher order derivatives, in general, it is not possible not to take into account the surface integrated term since it gives direct contribution to the forms of the…

For binary mixtures of fluids without chemical reactions, but with components having different temperatures, the Hamilton principle of least action is able to produce the equation of motion for each component and a balance equation of the…

Locomotion on small scales is dominated by the effects of viscous forces and, as a result, is subject to strong physical and mathematical constraints. Following Purcell's statement of the scallop theorem which delimitates the types of…

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…

Virtual constraints are relations imposed on a control system that become invariant via feedback control, as opposed to physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints…

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…

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…

The principle of least action provides a holistic worldview in which nature in its entirety and every detail is pictured in terms of actions. Each and every action is ultimately composed of one or multiples of the most elementary action…

The aim of this study is to present an alternative way to deduce the equations of motion of general (i.e., also nonlinear) nonholonomic constrained systems starting from the d'Alembert principle and proceeding by an algebraic procedure. The…

The main aim of the present paper is to raise the doubt that vakonomic dynamics may not be satisfactory as a model for velocity dependent constraints.

We first present a way to formulate the equations of motion for a nonholonomic system with nonlinear constraints with respect to the velocities. The formulation is based on the Cetaev condition which aims to extend the practical method of…

The so called ''Principle of the self-consistency'' for space-time models with causality violation, which was firstly formulated by I.D.Novikov, is discussed for the test particle motion and for test scalar field. It is shown that 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…

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 investigate the behavior of dynamical systems with nonholonomic constraints when coupled to a thermal bath, focusing on the paradigmatic case of the Chaplygin sleigh. A straightforward Langevin-type approach obtained by naively adding…

Every physical theory has (at least) two different forms of mathematical equations to represent its target systems: the dynamical (equations of motion) and the kinematical (kinematical constraints). Kinematical constraints are…

The paper is concerned with mechanical systems which are controlled by implementing a number of time-dependent, frictionless holonomic constraints. The main novelty is due to the presence of additional non-holonomic constraints. We develop…

The least action principle, through its variational formulation, possesses a finalist aspect. It explicitly appears in the fractional calculus framework, where Euler-Lagrange equations obtained so far violate the causality principle. In…