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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 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 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…
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 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 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…
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.…
The problem of constant-speed ballistics is studied under the umbrella of non-linear non-holonomic constrained systems. The Newtonian approach is shown to be equivalent to the use of Chetaev's rule to incorporate the constraint within the…
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 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…
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 derive conditions for a nonholonomic system subject to nonlinear constraints (obeying Chetaev's rule) to preserve a smooth volume form. When applied to affine constraints, these conditions dictate that a basic invariant density exists if…
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…
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…
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…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the…
We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for…
In this paper we have obtained some dynamics equations, in the presence of nonlinear nonholonomic constraints and according to a lagrangian and some Chetaev-like conditions. Using some natural regular conditions, a simple form of these…
Based on the d'Alembert-Lagrange-Poincar\'{e} variational principle, we formulate general equations of motion for mechanical systems subject to nonlinear nonholonomic constraints, that do not involve Lagrangian undetermined multipliers. We…