Related papers: On the Dynamics of a Rolling Ball Actuated by Inte…
The controlled motion of a rolling ball actuated by internal point masses that move along arbitrarily-shaped rails fixed within the ball is considered. Application of the variational Pontryagin's minimum principle yields the ball's…
The controlled motion of a rolling ball actuated by internal point masses that move along arbitrarily-shaped rails fixed within the ball is considered. The controlled equations of motion are solved numerically using a predictor-corrector…
The goal of this paper is to investigate the normal and tangential forces acting at the point of contact between a horizontal surface and a rolling ball actuated by internal point masses moving in the ball's frame of reference. The normal…
Using Euler's equations of motion and the Hamiltonian formulation, we obtain the equations of motion of systems with internal angular momentum that are moving with respect to a given reference frame, when subjected to a torque which is…
This paper presents a general formulation of equations of motion of a pendulum with n point mass by use of two different methods. The first one is obtained by using Lagrange Mechanics and mathematical induction(inspection), and the second…
In this paper we consider cases of existence of invariant measure, additional first integrals, and Poisson structure in a problem of rigid body's rolling without sliding on plane and sphere. The problem of rigid body's motion on plane was…
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…
The paper is concerned with the problem on rolling of a homogeneous ball on an arbitrary surface. New cases when the problem is solved by quadratures are presented. The paper also indicates a special case when an additional integral and…
We solve a set of selected exercises on rotational motion requiring a mechanical and thermodynamical analysis. When non-conservative forces or thermal effects are present, a complete study must use the first law of thermodynamics together…
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…
Using the Hamiltonian formulation, we have attempted to obtain the equations of motion of systems with internal angular momentum that are moving with respect to a reference system when subjected to an interaction. This interaction involves…
In this paper we study the controlled motion of an arbitrary two-dimensional body in an ideal fluid with a moving internal mass and an internal rotor in the presence of constant circulation around the body. We show that by changing the…
Three parameterizations are developed for modeling translational motion of a point mass in atmosphere flight over a central rotating body. Unlike well-known parameterizations such as spherical coordinate parameterizations, where position…
The purpose of the dynamics of moving systems is to search for the mathematical model that describes the link between the resultant applied force, that is the cause, and the speed of system that is the effect. This mathematical link…
This work investigates the dynamics of closed quantum systems in the Bloch vector representation using methods from rigid body dynamics and the theory of integrable systems. To this end, equations of motion for Bloch components are derived…
We consider a two-dimensional, incompressible fluid body, together with self-induced interactions. The body is perturbed by an external particle with small mass. The whole configuration rotates uniformly around the common center of mass. We…
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…
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…
An equation of motion of the mass point with internal degrees of freedom in scalar potential $U$ depending on relative coordinates and time, velocity and accelerations is obtained both for non-relativistic and relativistic case. In…
Euler-Poincare equations are derived for the dynamical folding of charged molecular strands (such as DNA) modeled as flexible continuous filamentary distributions of interacting rigid charge conformations. The new feature is that the…